abstract. A first-order dynamic epistemic logic is developed where the names of the agents are also terms in the sense of first-order logic. Consequently one can quantify over epistemic modalities. Us- ing constructs from dynamic logic one can express many interesting concepts. First-order update models are developed and added to the language as modalities.

Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: Language ℒ' is the least expressive extension of ℒ with interpolation. For instance, let ℳ be the extension of the basic modal language with a difference operator [7]. First-order logic is the least expressive extension of ℳ with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the (...) guarded fragment. (shrink)

In this paper we study the expressive power and definability for modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language.

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the (...) use of modal operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators. (shrink)

Does general validity or real world validity better represent the intuitive notion of logical truth for sentential modal languages with an actuality connective? In (Philosophical Studies 130:436–459, 2006) I argued in favor of general validity, and I criticized the arguments of Zalta (Journal of Philosophy 85:57–74, 1988) for real world validity. But in Nelson and Zalta (Philosophical Studies 157:153–162, 2012) Michael Nelson and Edward Zalta criticize my arguments and claim to have established the superiority of real world validity. Section (...) 1 of the present paper introduces the problem and sets out the basic issues. In Sect. 2 I consider three of Nelson and Zalta’s arguments and find all of them deficient. In Sect. 3 I note that Nelson and Zalta direct much of their criticism at a phrase (‘true at a world from the point of view of some distinct world as actual’) I used only inessentially in Hanson (Philosophical Studies 130:436–459, 2006), and that their account of the philosophical foundations of modal semantics leaves them ill equipped to account for the plausibility of modal logics weaker than S5. Along the way I make several general suggestions for ways in which philosophical discussions of logical matters–especially, but not limited to, discussions of truth and logical truth for languages containing modal and indexical terms–might be facilitated and made more productive. (shrink)

A system of modal logic with the operator is proposed, and proved complete. In contrast with a previous one by Stalnaker and Thomason, this system does not require two categories of singular terms.

All languages, both spoken and signed, make a formal distinction between two types of terms in a proposition – terms that identify what is to be talked about (nominals) and terms that say something about this topic (predicates). Here we explore conditions that could lead to this property by charting its development in a newly emerging language – Nicaraguan Sign Language (NSL). We examine how handshape is used in nominals vs. predicates in three Nicaraguan groups: (1) homesigners who (...) are not part of the Deaf com- munity and use their own gestures, called homesigns, to communicate; (2) NSL cohort 1 signers who fashioned the first stage of NSL; (3) NSL cohort 2 signers who learned NSL from cohort 1. We compare these three groups to a fourth: (4) native signers of American Sign Language (ASL), an established sign language. We focus on handshape in predicates that are part of a productive classifier system in ASL; handshape in these predicates varies sys- tematically across agent vs. no-agent contexts, unlike handshape in the nominals we study, which does not vary across these contexts. We found that all four groups, including home- signers, used handshape differently in nominals vs. predicates – they displayed variability in handshape form across agent vs. no-agent contexts in predicates, but not in nominals. Variability thus differed in predicates and nominals: (1) In predicates, the variability across grammatical contexts (agent vs. no-agent) was systematic in all four groups, suggesting that handshape functioned as a productive morphological marker on predicate signs, even in homesign. This grammatical use of handshape can thus appear in the earliest stages of an emerging language. (2) In nominals, there was no variability across grammatical con- texts (agent vs. no-agent), but there was variability within- and across-individuals in the handshape used in the nominal for a particular object. This variability was striking in homesigners (an individual homesigner did not necessarily use the same handshape in every nominal he produced for a particular object), but decreased in the first cohort of NSL and remained relatively constant in the second cohort. Stability in the lexical use of handshape in nominals thus does not seem to emerge unless there is pressure from a peer linguistic community. Taken together, our findings argue that a community of users is essential to arrive at a stable nominal lexicon, but not to establish a productive morpholog- ical marker in predicates. Examining the steps a manual communication system takes as it moves toward becoming a fully-fledged language offers a unique window onto factors that have made human language what it is. (shrink)

Sign language interpreting is a cognitively challenging task performed mostly by second language learners. SLI students must first gain language fluency in a new visuospatial modality and then move between spoken and signed modalities as they interpret. As a result, many students plateau before reaching working fluency, and SLI training program drop-out rates are high. However, we know little about the requisite skills to become a successful interpreter: the few existing studies investigating SLI aptitude in terms of (...) linguistic and cognitive skills lack baseline measures. Here we report a 3-year exploratory longitudinal skills assessments study with British Sign Language -English SLI students at two universities. Our aims were two-fold: first, to better understand the prerequisite skills that lead to successful SLI outcomes; second, to better understand how signing and interpreting skills impact other aspects of cognition. A battery of tasks was completed at four time points to assess skills, including but not limited to: multimodal and unimodal working memory, 2-dimensional and 3-dimensional mental rotation, and English comprehension. Dependent measures were BSL and SLI course grades, BSL reproduction tests, and consecutive SLI tasks. Results reveal that initial BSL proficiency and 2D-MR were associated with selection for the degree program, while visuospatial working memory was linked to continuing with the program. 3D-MR improved throughout the degree, alongside some limited gains in auditory, visuospatial, and multimodal working memory tasks. Visuospatial working memory and MR were the skills closest associated with BSL and SLI outcomes, particularly those tasks involving sign language production, thus, highlighting the importance of cognition related to the visuospatial modality. These preliminary data will inform SLI training programs, from applicant selection to curriculum design. (shrink)

It is widely assumed in the developmental literature that certain classes of modal expression appear later in language acquisition than others; specifically, epistemic interpretations lag behind non-epistemic interpretations. An explanation for these findings is proposed in terms of the child’s developing theory of mind, i.e. the ability to attribute to oneself and others mental representations, and to reason inferentially about them. It is hypothesized that epistemic modality crucially implicates theory-of-mind abilities and is therefore expected to depend on prior (...) developments in the child's ability to handle representations of mental representations. In support of this hypothesis, it is shown that autistic individuals have difficulty with epistemics. (shrink)

In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced in Andreas (Synthese 174(3):367–383, 2010). We will thereby show that the application to Peano arithmetic yields a formal semantics of universal structuralism, i.e., the view that ordinary mathematical statements in arithmetic express general claims about all (...) admissible interpretations of the Peano axioms. Moreover, we compare this application with the modal structuralism by Hellman (Mathematics without numbers: towards a modal-structural interpretation. Oxford University Press: Oxford, 1989), arguing that it provides us with an easier epistemology of statements in arithmetic. (shrink)

The essay discusses a recurrent criticism of the isomorphism-invariance criterion for logical terms, according to which the criterion pertains only to the extension of logical terms, and neglects the meaning, or the way the extension is fixed. A term, so claim the critics, can be invariant under isomorphisms and yet involve a contingent or a posteriori component in its meaning, thus compromising the necessity or apriority of logical truth and logical consequence. This essay shows that the arguments underlying the (...) criticism are flawed since they rely on an invalid inference from the modal or epistemic status of statements in the metalanguage to that of statements in the object-language. The essay focuses on McCarthy’s version of the argument, but refers to Hanson and McGee’s versions as well. (shrink)

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the (...) theoretical terms once these terms are introduced through the axioms of a theory. (shrink)

A concept language with role intersection and number restriction is defined and its modal equivalent is provided. The main reasoning tasks of satisfiability and subsumption checking are formulated in terms of modal logic and an algorithm for their solution is provided. An axiomatization for a restricted graded modal language with intersection of modalities (the modal counterpart of the concept language we examine)is given and used in the proposed algorithm.

First-order modal logics, as traditionally formulated, are not expressive enough. It is this that is behind the difficulties in formulating a good analog of Herbrand’s Theorem, as well as the well-known problems with equality, non-rigid designators, definite descriptions, and nondesignating terms. We show how all these problems disappear when modal language is made more expressive in a simple, natural way. We present a semantic tableaux system for the enhanced logic, and (very) briefly discuss implementation issues.

Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each (...) sentence of one language there is a sentence of the other language such that given any model, the former sentence is true at the actual world of the model iff the latter is? Forbes (1989) shows that this can be done by adding to both languages a pair of sentential operators called Vlach-operators, and imposing a syntactic restriction on their occurrences in formulas. As Forbes himself recognizes, this restriction is somewhat artificial. The first result I establish in this paper is that one gets sameness of expressivity by introducing infinitely many distinct pairs of indexed Vlach-operators. I then study the effect of adding to our enriched modal languages a rigid actuality operator. Finally, I discuss another means of enriching both languages which makes them expressively equivalent, one that exploits devices introduced in Peacocke (1978). Forbes himself mentions that option but does not prove that the resulting languages are equally expressive. I do, and I also compare the Peacockian and the Vlachian methods. In due course, I introduce an alternative notion of expressivity and I compare the Peacockian and the Vlachian languages in terms of that other notion. (shrink)

In the paper we introduce a wide range of Anderson-like variants of Gödel's theory and prove for each of them strong completeness theorem wrt. corresponding class of modal structures.These theories — all formulated in the 2nd order modal language with a 2nd order unary predicate of positiveness — differ among themselves with respect of: properties of the necessity operator and of the predicate of positiveness, axioms characterizing identity between 1st sort terms, definitions of identity between 2nd sort (...) terms, the treatment of Godlikeness as a term of the 2nd order, the treatment of necessary existence as a term of the 2nd order if there exists the necessity of its presence, the treatment of Ix (Ix(y) is read: terms x, y are identical), for every 1st sort term x, as a term of the 2nd order if there exists the necessity of its presence.Concerning to semantical commitments, the following are essential: (i) 1st order terms order receive only rigid extensions in the constant objectual 1st order domain; (ii) 2nd order terms receive non-rigid extensions in the constant objectual domain of 2nd order and rigid intensions in the constant conceptual 2nd order domain; (iii) The behavior of the identity between 1st sort terms shifts from possible worlds to possible worlds. (shrink)

Taboo terms offer a playground for linguistic creativity in language after language, and sign languages form no exception. The present paper offers the first investigation of taboo terms in sign languages from a cognitive linguistic perspective. We analyze the linguistic mechanisms that introduce offense, focusing on the combined effects of cognitive metonymy and iconicity. Using the Think Aloud Protocol, we elicited offensive or crass signs and dysphemisms from nine signers. We find that German Sign Language uses a (...) variety of linguistic means to introduce and enhance offense, many of which rely on iconic properties of the taboo sign. In conjunction with cross-linguistically common metonymic word-formation strategies, the degree of visual explicitness of a sign increases its potential to offend. Semantically similar taboo signs based on the same metonymic anchor but differing in their degree of iconicity also differ in offensiveness. This allows for creating dysphemisms and euphemisms via phonological changes to a sign. We further show that embodiment creates modality-enhanced ‘vicarious embarrassment’ in the viewer that results in the respective signs being judged obscene or offensive. Further, lexical blending and non-manual enhancement play a role in the creation of dysphemisms in DGS. Lastly, we propose that iconicity as a cognitive structuring principle of linguistic expressions constrains the possible semantic extensions of iconic taboo terms. (shrink)

This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction and elimination rules for modalities are based on the polymorphism of terms in the language. This leads to a (...) multi-modal non-homogeneous version of a type theory, in which we show the embedding of the modal operators into standard group knowledge operators. (shrink)

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for (...) their primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

The dissertation gives a second-order-logic-based explanation of modal incompleteness. The leading concept is that modal incompleteness is to be explained in terms of the incompleteness of standard second-order logic, since modal language is basically a second-order language. The development of Kripke-style semantics for modal logic has been underpinned by the conjecture that all modal systems are characterizable by classes of frames defined by first-order conditions on a binary relation. However, the discovery of certain (...) incomplete modal systems has undermined the all-encompassing feature of Kripke-style approach. There are logics not determined by any class of Kripke frames at all. ;In the dissertation I investigate a normal incomplete sentential modal system due to J. F. A. K. Van Benthem, and I address both the formal and the philosophical facets of modal incompleteness from the vantage point that modal logic is essentially second-order in its nature. Modal systems can be analyzed in terms of structures with a domain of second-order individuals that are assigned under an interpretation to propositional variables within languages of sentential modal logic. Hence, the phenomenon of there being incomplete modal systems can be accounted for through the incompleteness of standard second-order logic. ;Since second-order logic plays a crucial role in the explanation, Quine's animadversions upon second-order logic and in particular his views that second-order logic is 'Set Theory in Sheep's Clothing' are examined. Against Quine's stance I will seek to show that a vindication of second-order logic can be gotten provided a proper due is given to the sharp distinction between the logical notion of set which is the concern of second-order logic and the iterative notion of set which lies within the realm of set theory. (shrink)

This paper articulates the structure of a two species of weakly aggregative necessity in a common idiom, neighbourhood semantics, using the notion of a k-filter of propositions. A k-filter on a non-empty set I is a collection of subsets of I which contains I, is closed under supersets on I, and contains ∪{Xi ≤ Xj : 0 ≤ i < j ≤ k} whenever it contains the subsets X0,…, Xk. The mathematical content of the proof that weakly aggregative modal (...) logic is complete relative to k-ary frame theory, the standard semantic idiom for weakly aggregative modal logic is presented in language-independent terms as a representation theorem for k-filters: every non-trivial k-filter is included in the union of ≤ k non-trivial filters. The elementary theory of k-filters is developed and then applied in the form of an ultrafilter extension result for k-ary frame theory. (shrink)

In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication (...) is weaker than the material one. In the final section, we present a tableau approach to the discussed modal logics. (shrink)

In the past three decades there has been a rapid development of the formal machinery for modal logic. Quantified modal logic has developed along with a semantics and model theory that is appropriate to it. With this technical development there has been relatively little discussion of what modality is all about. There are two fundamental questions that have gone unanswered. First, to what does necessity amount? Is this a new logical notion, or is it something that can be (...) further analyzed in terms of other notions that we already have at our disposal? The second question is what makes truths involving necessity true? What is their ontological grounding in the world? This essay is directed at the first of these questions. ;There are three possible reductions of metaphysical modality. First, there is the reduction suggested by the semantics for modal logic: a reduction in terms of possible worlds. Second, there is the reduction in terms of cognition. What is possible is what is conceivable. Third, there is the reduction in terms of language. Necessities arise from the structures of language and/or language use. ;I argue that none of these is successful. All of them suffer either from presupposing some form of metaphysical necessity in the reductive base, rendering them circular and not truly reductive, or they do not do justice to the modality being reduced. ;Since necessity is not reducible to any non-modal features of the world, we need to determine whether we ought to reject it as unacceptable on this basis, or whether we ought to retain it, but treat is as a new primitive that is introduced into a philosophical or logical theory. I urge the latter course is the one that we ought to take because without it too many things will likewise be deemed unacceptable. Causal necessity and explanation, normally accepted theories or knowledge and perception, logic and logical validity, and one common manner of distinguishing sets from properties will be deemed unacceptable if de re necessity is unacceptable. All of these presuppose de re metaphysical necessity in some way. I conclude that de re metaphysical necessity ought to be retained in our theory as primitive, unanalyzable notion. (shrink)

In this volume, the author investigates and argues for, a particular answer to the question: What is the right way to logically analyze modalities from natural language within formal languages? The answer is: by formalizing modal expressions in terms of predicates. But, as in the case of truth, the most intuitive modal principles lead to paradox once the modal notions are conceived as predicates. -/- The book discusses the philosophical interpretation of these modal paradoxes and (...) argues that any satisfactory approach to modality will have to face the paradoxes independently of the grammatical category of the modal notion. By systematizing modal principles with respect to their joint consistency and inconsistency, Stern provides an overview of the options and limitations of the predicate approach to modality that may serve as a useful starting point for future work on predicate approaches to modality. Stern also develops a general strategy for constructing philosophically attractive theories of modal notions conceived as predicates. The idea is to characterize the modal predicate by appeal to its interaction with the truth predicate. This strategy is put to use by developing the modal theories Modal Friedman-Sheard and Modal Kripke-Feferman. (shrink)

I propose and defend an account on which the semantic content of propositions expressed by utterances making use of modals epistemically is constant; i.e., invariant. Although such proposals are typically considered non-starters, I aim to show that combining such a semantics with a performative account in which such utterances perform two speech acts is quite promising. I argue that a performative account, when combined with an invariant semantic content theory, does a good job of accounting for ordinary intuitions in some (...) of the standard test cases discussed in the literature. I further show that the contextualist has a little noticed problem with how a single speaker is able to consider the same epistemic possibility proposition over time. An invariant position has no such problem, and I argue that this counts strongly in its favor. (shrink)

Let us sum up. We began with the question, “What is the interest of a model-theoretic definition of validity?” Model theoretic validity consists in truth under all reinterpretations of non-logical constants. In this paper, we have described for each necessity concept a corresponding modal invariance property. Exemplification of that property by the logical constants of a language leads to an explanation of the necessity, in the corresponding sense, of its valid sentences. I have fixed upon the epistemic modalities (...) in characterizing the logical constants: to be a logical constant in the language of a population is to be invariant over a modality describing complete possible epistemic states of that population (or an idealized analogue thereof). The grounds for this characterization are these: (1) It leads, I believe, to an extensionally reasonable demarcation of the logical constants, including clear cases and excluding clear non-cases. It gives a principled criterion for deciding unclear cases. (2) It provides an analysis of the topic-neutrality of logic. (3) It leads to an explanation of the epistemic necessity of the logical truths in terms of the topic-neutrality of the logical constants.All the same, it is reasonable to ask, even if the suggested demarcation of logic is extensionally correct, whether it can reasonably be expected to be fundamental. The epistemic invariance of an expression is a rather striking property, one which we should want to explain. What is missing, then, is an explanation of the distinguishing epistemic properties of the constants in terms of more fundamental properties involving their understanding and use. It would be these that properly define the nature, not just the extent, of logic. (shrink)

The present paper studies formal properties of so-called modal information logics (MILs)—modal logics first proposed in (van Benthem 1996 ) as a way of using possible-worlds semantics to model a theory of information. They do so by extending the language of propositional logic with a binary modality defined in terms of being the supremum of two states. First proposed in 1996, MILs have been around for some time, yet not much is known: (van Benthem 2017, 2019 ) (...) pose two central open problems, namely (1) axiomatizing the two basic MILs of suprema on preorders and posets, respectively, and (2) proving (un)decidability. The main results of the first part of this paper are solving these two problems: (1) by providing an axiomatization [with a completeness proof entailing the two logics to be the same], and (2) by proving decidability. In the proof of the latter, an emphasis is put on the method applied as a heuristic for proving decidability ‘via completeness’ for semantically introduced logics; the logics lack the FMP w.r.t. their classes of definition, but not w.r.t. a generalized class. These results are build upon to axiomatize and prove decidable the MILs attained by endowing the language with an ‘informational implication’—in doing so a link is also made to the work of (Buszkowski 2021 ) on the Lambek Calculus. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence (...) according to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics (...) for predicates of sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (shrink)

Forensic authorship analysis is based on two assumptions: that every individual has a unique idiolect, and that features characteristic of that idiolect will recur with a relatively stable frequency. Yet, a speaker’s language can change with age, affective states, according to audience, or genre. Thus, studies on authorship analysis should adopt the theory that while some linguistic parameters of an idiolect can remain stable, others can change depending on various circumstances. This investigation, which takes a constructional and functional-based approach (...) to discourse-level phenomena in idiolectal stability, analyzes cross-genre data produced by nine Mexican participants throughout a twelve-year time span. This study contributes to a greater understanding of the linguistic elements that survive genre effects and are potentially useful in both investigative and evidential forensic linguistic work. We provide a detailed description of linguistic features, their specific values, and context-dependent interpretation, keeping in mind the context of expert linguistic testimony, with its preference for methods which “employ linguistically motivated analyses in combination with quantitative tools” (Solan & Tiersma, 2004, p.463). Our findings show that idiolectal style tends to remain stable across genres and communication modes in epistemic modality constructions. Epistemic markers —specifically, markers indicating low commitment by the speaker (e.g., _no sé_ ‘I don’t know’) or expressing indirectness when introducing the illocutionary force (e.g., _la verdad [es que]_ ‘the truth [is that]’)— display idiolectal stability, as these markers seem to be the most effective in terms of allowing speakers to strategically manifest the extent of their knowledge regarding what is said. (shrink)

We shall be concerned with the modal logic BK—which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding ‘strong negation’. Though all four values ‘truth’, ‘falsity’, ‘neither’ and ‘both’ are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for ‘neither’ or/and ‘both’ leads to quite unexpected results. (...) To be more precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics. (shrink)

(1) modal logic is not needed, Since there are alternative accounts of modality. (2) modal logic does not function as logic even in the thinking of its advocates, As is revealed, E.G., When the semantics of modal logic is presented in an extensional metalanguage. Furthermore, (3) when a wider view is taken, One sees that modal logic treats as logical constants expressions that belong to a large and open syntactic class, Unlike other logical constants. Finally, (4) (...) modal logic treats as sentential operators devices that function in natural language as underlying predicates. The last two points also indicate that a theory of modality making use of modal predicates is to be preferred to an account that explains away modality in terms of quantification over possible worlds. (shrink)

This paper argues for a largely unnoted distinction between relational and modal components in the lexical semantics of verbs. Wehypothesize that many verbs encode two kinds of semantic information:a relationship among participants in a situation and a subset ofcircumstances or time indices at which this relationship isevaluated. The latter we term sublexical modality.We show that linking regularities between semantic arguments andsyntactic functions provide corroborating evidence in favor of thissemantic distinction, noting cases in which the semantic groundingof linking through (...) participant-role properties apparently fails. Thissemantic grounding can be preserved, however, once we abstractaway from sublexical modality in lexical semantic representations.Semantically-based linking constraints are insensitive to the sublexicalmodality component of lexical entries and depend only on informationin a predicator's situational core. (shrink)

We present a general approach to quantified modal logics that can simulate most other approaches. The language is based on operators indexed by terms which allow to express de re modalities and to control the interaction of modalities with the first-order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between n-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many, or no object in an accessible (...) world. Moreover by taking as primitive a relation between n-tuples we avoid some shortcoming of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete quantified modal logics. (shrink)

Gideon Rosen described the difficulties faced by those who claim that statements about possible worlds cannot be literally true. According to his argument, if the truth of modal sentences could be explained by referring to the hypothesis of the plurality of possible worlds, which is a sort of fiction for modal irrealists, the position would have antinomic consequence. I argue that the advocate of broad modal fictionalism can avoid such a devastating conclusion. To that end, her position (...) should be given in meta-language describing the necessary and sufficient conditions of accepting modal sentences as true in terms of fiction of possible worlds. I show that there is a coherent way of reading ‘it is accepted as true’ that allows one to maintain that the disjunction of two mutually contradictory propositions can be accepted without accepting either of them. (shrink)

This paper provides a semantic analysis of the particles afinal (European Portuguese) and alla fine (Italian) in terms of the notion of truth unpersistence, which can be situated at the intersection of epistemic modality and discourse structure. In the analysis proposed, the particles are propositional operators and require that the truth of a proposition p* fail to persist through a temporal succession of epistemic states, this proposition being incompatible with the prejacent, and that the interlocutors share knowledge of a previous (...) epistemic attitude toward p*. We analyze two main cases (plan-related and non plan-related propositions) and also show that these particles are indexical to one (or more) epistemic agent(s) and allow for shifts in perspective. (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth (...) collapses to truth. Then I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)

Philosophical discussions of mechanisms and mechanistic explanation have often been framed by contrast to laws and deductive-nomological explanation. A more adequate conception of lawfulness and nomological necessity, emphasizing the role of modal considerations in scientific reasoning, circumvents such contrasts and enhances understanding of mechanisms and their scientific significance. The first part of the paper sketches this conception of lawfulness, drawing upon Haugeland, Lange, and Rouse. This conception emphasizes the role of lawful stability under relevant counterfactual suppositions in scientific reasoning (...) across the sciences, in place of traditional conceptions of law that are primarily confined to the physical sciences. It also extends lawful stability beyond verbally or mathematically expressed law-statements, to encompass other ways of conjoining patterns in the world with scientific pattern recognition. The remainder of this paper shows how and why mechanisms constructively exemplify this conception of lawfulness in scientific practice: • Mechanisms are robust, counterfactually stable and inductively projectible patterns, even though they are not exceptionless “laws of nature”. • Mechanistic explanations often take non-verbal forms, which consequently resist philosophical inclinations to semantic ascent, but understanding lawfulness in terms of counterfactually stable pattern recognition accounts for these ways in which scientific understanding outruns the expressive capacities of natural languages; • Mechanisms are sometimes characterized as real patterns in the world, and sometimes as epistemic representations; understanding mechanisms as modal patterns shows why both conceptions are needed, as mutually supportive. • Mechanisms are typically open-ended, and only partially specified, in ways open to and directive toward further articulation and revision. Understanding mechanisms as modal patterns incorporates this aspect of mechanistic understanding within a broader conception of scientific understanding as embedded in research practice, rather than in bodies of knowledge extracted from it. • Mechanistic explanation has often been placed on the causal side of an opposition between causal and nomological explanation, but understanding mechanisms as modal patterns helps overcome that opposition, and contributes to a pluralist conception of causal relations and their characteristic forms of counterfactual invariance. • The recognition of mechanisms as modal patterns allows for a new way to think about the relations among distinct levels of a mechanistic hierarchy, and the broader scientific significance of mechanistic understanding. (shrink)

This paper introduces a new method of interpreting complex relation terms in a second-order quantified modal language. We develop a completely general second-order modal language with two kinds of complex terms: one kind for denoting individuals and one kind for denoting n-place relations. Several issues arise in connection with previous, algebraic methods for interpreting the relation terms. The new method of interpreting these terms described here addresses those issues while establishing an interesting connection between λ and (...) ε calculi. The resulting semantics provides a precise understanding of the theory of relations. (shrink)

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is (...) formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system. (shrink)

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new (...) proof of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)

This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ, where x occurs only positively in γ, we obtain the flat modal fixpoint language by adding to the language of polymodal logic a connective γ for each γΓ. The term γ is meant to be interpreted as the least fixed point of the functional interpretation of the (...) term γ. We consider the following problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen–Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite. (shrink)

Counterpossibles are counterfactuals that involve some metaphysical impossibility. Modal normativism is a non-descriptivist account of metaphysical necessity and possibility according to which modal claims, e.g. ‘necessarily, all bachelors are unmarried’, do not function as descriptive claims about the modal nature of reality but function as normative illustrations of constitutive rules and permissions that govern the use of ordinary non-modal vocabulary, e.g. ‘bachelor’. In this paper, I assume modal normativism and develop a novel account of counterpossibles (...) and claims about metaphysical similarity between possible and impossible worlds. I argue that considerations of metaphysical similarity between various impossible worlds and the actual world only require us to tacitly consider how the actual constitutive rules that govern the use of our terms change in order to accommodate the description of some hypothetical impossible scenario. I then argue for my account by raising worries for alternative epistemic and realist accounts of counterpossibles and showing how my account avoids those worries. (shrink)

Despite the wide acceptance of standard modal logic, there has always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators. The aim of the formal model outlined in this paper is to capture what I take to be the only plausible sense in which ‘possible’ and ‘necessary’ can be treated as predicates. The model is built by enriching the language of (...) standard modal logic with a quantificational apparatus that is “substitutional” rather than “objectual”, and by obtaining from the language so enriched another language in which constants for such predicates apply to singular terms that stand for propositions. (shrink)

Saul Kripke’s thesis that ordinary proper names are rigid designators is supported by widely shared intuitions about the occurrence of names in ordinary modal contexts. By those intuitions names are scopeless with respect to the modal expressions. That is, sentences in a pair like (a) Aristotle might have been fond of dogs (b) Concerning Aristotle, it is true that he might have been fond of dogs will have the same truth value. The same does not in general hold (...) for definite descriptions. If we, like Kripke, account for this difference by means of the intensions of names and descriptions, we have to conclude that names do not in general have the same intension as any normal, identifying description. However, the difference in scope behavior between names and description can be accounted for alternatively by appeal to the semantics of the modal expressions. On the account we suggest, dubbed ‘relational modality’, simple singular terms, like proper names, contribute to modal contexts simply by their actual world reference, not by their (standard) intension. The relational modality account turns out to be fully equivalent with the rigidity account when it comes to truth of modal and non-modal sentences (with respect to the actual world), and hence supports the same basic intuitions. Given an alternative definition of consequence for relational modality, and a restriction to models with reflexive accessibility relations and non-empty world-bound domains, relational modality also turns out to be model theoretically equivalent with rigidity semantics with respect to logical consequence. Here we introduce the semantics, give the truth definition for relational modality models, and prove the equivalence results. (shrink)

The English perfect involves two fundamental components of meaning: a truth-conditional one involving temporal notions and a current relevance presupposition best expressed in terms drawn from the analysis of modality. The proposal made here draws much for the Extended Now theory (McCoard 1978 and others), but improves on it by showing that many aspects of the perfect's meaning may be factored out into independent semantic or pragmatic principles.

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.1 (2001) 121-140 [Access article in PDF] The Rhetoric of Modal Equivocacy in Cartesian Transubstantiation Julian Bourg Everyday language, in which words are not defined, is a medium in which nobody can express himself unequivocally. Robert Musil 1René Descartes's attempt to explain Eucharistic transubstantiation has long been understood as a dramatically significant moment in his tightrope walk across the medieval-to-modern divide. (...) 2 Modeled on the Last Supper in the New Testament, the Eucharistic rite had been explained in the Catholic tradition after the twelfth century in the scholastic philosophical language of substance and accident. 3 As the Council of Trent reaffirmed in 1551, this transubstantiation was a conversion "of the whole substance of the bread into the substance of the Body and of the whole substance of the wine into the substance of His blood... the appearances [speciebus] only of the bread and wine remaining." 4 Christ was [End Page 121] held to be "truly, really, and substantially contained under the species of those sensible things," under what still appeared to be bread and wine. 5Descartes's dilemma was that on one hand he was dead set against the hylomorphic theory of substance and accident, and on the other hand he found himself obliged by some of his interlocutors to comment on transubstantiation. It was a balancing act that pleased no one for very long, since despite his sometimes eager discussions of the Eucharist, he was not, as he admitted, "a theologian by profession." 6 The putative heterodoxy of Cartesian transubstantiation was principally responsible for his works being placed on the Index of Prohibited Books in 1663 and for his thought being banned from schools under Louis XIV in 1671. 7 His treatment of the Eucharistic question also distressed others in the seventeenth and early eighteenth centuries, such as Thomas Hobbes and Isaac Newton, who were unhappy that Descartes had bothered with such a theological non-issue. 8 For the many post-seventeenth-century advocates of a proto-secular Descartes as the godfather of modern philosophy, Cartesian transubstantiation has proved similarly inconvenient.The indisputable connections between Descartes and his scholastic forerunners, exemplified by the Eucharistic question, service a basic question of contemporary Cartesian scholarship. As Émile Boutroux put it, how was new wine poured from old bottles? 9 Accepting as axiomatic that there was something both radical and original in the Cartesian project but without falling back on pieties about his turn toward the modern subject, we must ask how Descartes put forth novel claims in conceptual language regarded by his contemporaries as resonant, if not consonant, with the scholastic intellectual culture of Catholic Reform France. More precisely, setting aside the not-very-defensible position that such language was merely incidental to Cartesian thought (a position that dehistoricizes Descartes as a precocious Enlightener), the dilemma then becomes explaining how original positions were elaborated within scholastic language. One important task is accounting for what Descartes did with that vocabulary--how he pointed words and concepts in new and surprising directions. The Eucharist becomes crucial in this perspective. [End Page 122]Though the question of Cartesian transubstantiation has been discussed for some time, the topic is worth revisiting again in light of two themes, rhetoric and the Cartesian theory of modes. My argument is that Descartes used one particular scholastic term, "mode," in equivocal ways and that this equivocation was in multiple senses rhetorical. This rhetoric coalesced and came to the fore around the Eucharist because, given the intellectual-political climate of the Catholic Reformation, the stakes of transubstantiation were so high. That Descartes used certain scholastic terms in equivocal or ambiguous ways should come as no surprise. Of interest, though, is the fact that by definition "mode" meant many things. This ambiguous term facilitated ambiguous intellectual positions about the Eucharist that allowed Descartes more generally (no matter what he "really" intended) to skirt between an orthodoxy that represented the past and an originality, not without dangers in his time, that seem to gesture toward our day. Foregrounded with regard to... (shrink)

This chapter examines modality in the history of analytic philosophy. There were, in this history, two principal types of reductionism or eliminativism about modality, and two corresponding phases in the rejection of anti-modal stances. First, the founders of analytic philosophy, Frege, Moore, and Russell, took necessity and possibility to be reducible to more fundamental logical notions, where logic for these thinkers consists of truths about a mind- and language-independent reality extending beyond the empirical world. Against this reductionism, C. (...) I. Lewis and Wittgenstein argued that logic itself requires modal notions. Second, Carnap advanced a pragmatically motivated account of modal terms as expressing pseudo-object properties, which appear to be properties of objects but can be construed as properties of their designations. Quine criticized this account and proposed a thoroughgoing elimination of modality. Quine’s well-known claim that quantifying into modal contexts is unintelligible without resorting to essentialism cannot be fully understood independently of Carnap’s notion of pseudo-object property. Against Quine, Ruth Marcus and Saul Kripke argued for the coherence of modal concepts and their entrenchment in ordinary language and thought, leading to the now dominant view that modal properties are mind- and language-independent features of the world. (shrink)

Drawing an analogy between modal structuralism about mathematics and theism, I o er a structuralist account that implicitly de nes theism in terms of three basic relations: logical and metaphysical priority, and epis- temic superiority. On this view, statements like `God is omniscient' have a hypothetical and a categorical component. The hypothetical component provides a translation pattern according to which statements in theistic language are converted into statements of second-order modal logic. The categorical component asserts the logical (...) possibility of the theism struc- ture on the basis of uncontroversial facts about the physical world. This structuralist reading of theism preserves objective truth-values for theistic statements while remaining neutral on the question of ontology. Thus, it o ers a way of understanding theism to which a naturalist cannot object, and it accommodates the fact that religious belief, for many theists, is an essentially relational matter. (shrink)

One can add the machinery of relation symbols and terms to a propositional modal logic without adding quantifiers. Ordinarily this is no extension beyond the propositional. But if terms are allowed to be non-rigid, a scoping mechanism (usually written using lambda abstraction) must also be introduced to avoid ambiguity. Since quantifiers are not present, this is not really a first-order logic, but it is not exactly propositional either. For propositional logics such as K, T and D, adding such machinery (...) produces a decidable logic, but adding it to S5 produces an undecidable one. Further, if an equality symbol is in the language, and interpreted by the equality relation, logics from K4 to S5 yield undecidable versions. (Thus transitivity is the villain here.) The proof of undecidability consists in showing that classical first-order logic can be embedded. (shrink)