In this paper, we discuss some formal properties of the model ofbidirectional Optimality Theory that was developed inBlutner (2000). We investigate the conditions under whichbidirectional optimization is a well-defined notion, and we give aconceptually simpler reformulation of Blutner's definition. In thesecond part of the paper, we show that bidirectional optimization can bemodeled by means of finite state techniques. There we rely heavily onthe related work of Frank and Satta (1998) about unidirectionaloptimization.

One of three distinct approaches to his famous ‘Trust’ argument, this paper written by Garfinkel in 1960, and never before published, proposed a rethinking of rules, games and linguistic classifications in interactional terms consistent with Wittgenstein’s language games. Garfinkel had been working in collaboration with Parsons since 1958 to craft an approach to culture that would replace conceptual classification with the constitutive expectancies of interaction and systems of interaction. The argument challenged the work of cultural anthropologists influenced by zoology and (...) biology, who called themselves ‘ethnoscientists’ and studied culture in terms of linguistic classification systems. Garfinkel had proposed an alternative sociological ‘ethnoscience’ of culture and language that would focus on how culture was made, on how linguistic events are achieved, and on the rules of their making. This ‘Language Games’ approach followed Wittgenstein in seeking what Garfinkel called a literal description of cultural/linguistic events: meaning by ‘literal’, a step-by-step account of the constitutive and preferred rules participants use to create a recognizable event-in-a-language. Made famous three years later in version associated with Schutz, Garfinkel’s Trust argument also appears in a 1962 text (Parsons’ Primer, published in 2019) in a version built on Parsons. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the (...) psychology of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)

Can we employ the property of rationality in establishing what rationality requires? According to a central and formal thesis of John Broome’s work on rational requirements, the answer is ‘no’ – at least if we expect a precise answer. In particular, Broome argues that (i) the property of full rationality (i.e. whether or not you are fully rational) is independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. That is, (ii) (...) by replacing a wide-scope requirement with a corresponding narrow-scope requirement (or vice versa), we do not alter the situations in which a person is fully rational. As a consequence, (iii) the property of full rationality is unable to guide us in determining whether a rational requirement has a wide or a narrow logical scope. We cannot resolve the wide/narrow scope debate by appealing to a theory of fully rational attitudes. This paper argues that (i), (ii) and (iii) are incorrect. Replacing a wide- with a corresponding narrow-scope requirement (or vice versa) can alter the set of circumstances in which a person is fully rational. The property of full rationality is therefore not independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. As a consequence, the property of full rationality can guide us in determining what rationality requires – even in cases where we expect a precise answer. (shrink)

This paper proposes a concept of creativity that stems from a semiotic and linguistic theoretical perspective, in which the formal frame of reference for variation and linguistic change considers and evaluates both the process of general interaction and the contact of languages as a global phenomenon. This method proposes an analysis of creativity that ranges from reflections of ancient philosophy to a contemporary linguistic perspective, incorporates international ideologies, and identifies, within the dimensions of use and social sharing, the (...) principle capable of guiding potentially unlimited forms of linguistic creativity that are self-expressive and communicative, far beyond the grammatical patterns of regularity and norm. Interpreting the paradigm of creativity according to this model means placing the semiotic property in a position of prima inter pares, entrusted not only with the “role” of forming signs (words, sentences, texts), but the function of arbitraire, as a phenomenon of language creation. The following reading references the semiotic contribution of Tullio De Mauro, an Italian linguist who has contributed to the systematization of creativity, overcoming and synthesizing both Saussurian structuralism and Chomskyan generativism. (shrink)

Kind representations, concepts like table, triangle, dog, and planet, underlie generic language. Here, we investigate the formal structure of kind representations—the structure that distinguishes kind representations from other types of representations. The present studies confirm that participants distinguish generic‐supporting properties of individuals (e.g., this watch is made of steel) and accidental properties (e.g., this watch is on the nightstand). Furthermore, work dating back to Aristotle establishes that only some generic‐supporting properties bear a principled connection to the (...) kind, that is, are true of an individual by virtue of its being a member of a specific kind (e.g., telling time for a watch). The present studies tested the hypothesis that principled connections are part of the formal structure of kind representations. Specifically, they tested whether they structure a newly learned kind representation. Experiment 1 found that introducing a property of a newly encountered novel kind in any one of four linguistic frames that provide evidence that a property has a principled connection to a kind (e.g., “It has fur because it is a blick”) led participants to infer a different conceptual consequence of principled connections (i.e., “There is something wrong with this blick, which does not have fur”) for which they had no direct evidence. Two introduction frames that provided no evidence for principled connections (e.g., “Almost all blicks have fur”) did not generate the same consequence. Experiment 2 found that all of the targeted properties were generic licensing, irrespective of the introduction frame. That the distinction between properties that bear principled connections to their kinds, and merely generic‐supporting properties structures novel kind representations, provides strong evidence that this distinction is part of the formal structure of kind representations. (shrink)

We can distinguish different senses in which a formal language can be said to have been provided with an interpretation. We focus on two: (i) We provide a model (or structure) and a definition of satisfaction and truth in the standard way (ii) We provide a translation into a natural language. We argue that the sentences of a formal language interpreted as in (i) do not have meaning. A formal language interpreted as in (i) models the way (...) the truth of a sentence would be affected by two factors: the interpretation as in (ii) of the language, and a way the world might be. Viewing in this way the relation between interpreting a formal language as in (i) and as in (ii) allows us to justify the conceptual adequacy of the standard model-theoretic definitions of the properties of logical truth and logical consequence. (shrink)

Neural networks are widely used in systems of artificial intelligence, but due to their black box nature, they have so far evaded formal analysis to certify that they satisfy desirable properties, mainly when they perform critical tasks. In this work, we introduce methods for the formal analysis of reachability and robustness of neural networks that are modeled as rational McNaughton functions by, first, stating such properties in the language of Łukasiewicz infinitely-valued logic and, then, using the (...) reasoning techniques of such logical system. We also present a case study where we employ the proposed techniques in an actual neural network that we trained to predict whether it will rain tomorrow in Australia. (shrink)

This paper describes an axiomatic theory BT, which is a suitable formal theory for developing constructive mathematics, due to its expressive language with countable number of set types and its constructive properties such as the existence and disjunction properties, and consistency with the formal Church thesis. BT has a predicative comprehension axiom and usual combinatorial operations. BT has intuitionistic logic and is consistent with classical logic. BT is mutually interpretable with a so called theory of arithmetical (...) truth PATr and with a second-order arithmetic SA that contains infinitely many sorts of sets of natural numbers. We compare BT with some standard second-order arithmetics and investigate the proof-theoretical strengths of fragments of BT, PATr and SA. (shrink)

This paper explores the link between rules of grammar, grammar formalisms and the architecture of the language faculty. In doing so, it provides a flexible meta-level theory of the language faculty through the postulation of general axioms that govern the interaction of different components of grammar. The idea is simply that such an abstract formulation allows us to view the structure of the language faculty independently of specific theoretical frameworks/formalisms. It turns out that the system of rules, axioms and constraints (...) of grammar cannot beexplicitlyrepresented in a general architecture of the language faculty — which circumvents the ontological mismatch of mental representations and formal/axiomatic properties of language. Rather, the system of rules, axioms, constraints of grammar isintentionallyprojected by humans, and this projection realizes/instantiates what Dascal (1992) calls ‘psychopragmatics’. Relevant implications for linguistic theory, learnability and (computational) models of language processing are also explored. (shrink)

Words associated with perceptually salient, highly imageable concepts are learned earlier in life, more accurately recalled, and more rapidly named than abstract words (R. W. Brown, 1976; Walker & Hulme, 1999). Theories accounting for this concreteness effect have focused exclusively on semantic properties of word referents. A novel possibility is that word structure may also contribute to the effect. We report a corpus-based analysis of the phonological and morphological structures of a large set of nouns with imageability ratings (N (...) = 2,023). High- and low-imageability nouns differed by length, etymology, prosody, affixation, phonological neighborhood density, and rates of consonant clustering. On average, nouns denoting abstract concepts were longer, more derivationally complex, and emerged in English from a different distribution of languages than did concrete nouns. We address implications for interactivity of word form and meaning as pertain to theories of word concreteness, lexical acquisition, and word processing. (shrink)

Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different such tools are being increasingly used in order to accelerate and simplify proof checking, and the Coq proof assistant is one of the most well known and used in large-scale projects. Language and automata theory is a well-established area of mathematics, relevant to computer science foundations and information technology. In particular, context-free language (...) theory is of fundamental importance in the analysis, design, and implementation of computer programming languages. This work describes a formalization effort, using the Coq proof assistant, of fundamental results of the classical theory of contextfree grammars and languages. These include closure properties (union, concatenation, and Kleene star), grammar simplification (elimination of useless symbols, inaccessible symbols, empty rules, and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. As it turns out, this is a comprehensive formalization of the classical context-free language theory in the Coq proof assistant and includes the formalization of the Pumping Lemma for context-free languages. The perspectives for the further development of this work are diverse and can be grouped in three different areas: inclusion of new devices and results, code extraction, and general enhancements of its libraries. (shrink)

This book explores issues at the core of modern linguistics and cognitive science. Why are all languages similar in some ways and in others utterly different? Why do languages change and change variably? How did the human capacity for language evolve, and how far did it do so as an innate ability? Simon Kirby looks at these questions from a broad perspective, arguing that they can be studied together. The author begins by examining how far the universal (...) class='Hi'>properties of language may be explained by examining the way it is used, and how far by the way it is structured. He then considers what insights may be gained by combining functional and formal approaches. In doing so he develops a way of treating language as an adaptive system, in which its communicative and formal roles are both crucial and complementary. In order to test the effectiveness of competing theories and explanations, Simon Kirby develops computational models to show what universals emerge given a particular theory of language use or acquisition. He presents here both the methodology and the results. Function, Selection, and Innateness is important for its argument, its methodology, and its conclusions. It is a powerful demonstration of the value of looking at language as an adaptive system and goes to the heart of current debates on the evolution and nature of language. (shrink)

In this paper it is championed that a two stages hypothesis for the evolution of language must take into account a qualified approach to heterochrony and the available information from the archaeological record. As it seems, a protracted childhood and youth was already at work in Homo erectus, but early postnatal brain growth was only available to Homo sapiens. According to these facts, the term hysteron proteron is given here to the reversal that sets off linguistic capacity during the first (...) three years of life, upon the ancient abilities for social, natural and technological knowledge, which were already established during the last 2 Mya BP. The unfolding of linguistic capacity creates the typical effect that ontogeny reverses phylogeny: since late postnatal brain growth, quite recent in evolution, launches in ontogeny before the phylogenetically old processes of playing and learning take place during childhood and youth. Full symbolic abilities may be explained as emerging from older semiotic competences based on iconicity and indexicality, which would have presumably sustained human life for millennia. Furthermore, it is argued that the formation of linguistic categories follows from that overlaying of extended connectivity linked to early postnatal brain growth, inasmuch as it entangles and transforms previous iconic and referential information: i.e. the ancient semiotic capacities for proprioception, embodiment, extended mimesis and pragmatic knowledge, shaping a sort of self-organization process that provides the formal and semantic properties we find in articulated languages. (shrink)

Natural language meaning has properties of both (embodied) cognitive representations and formal/mathematical structures. But it is not clear how they actually relate to one another. This article argues that how properties of cognitive representations and formal/mathematical structures of natural language meaning can be united remains one of the puzzles in cognitive science. That is primarily because formal/mathematical structures of natural language meaning are abstract, logical, and truth‐conditional properties, whereas cognitive/conceptual representations are embodied and grounded (...) in sensory‐motor systems. After reviewing the current progress, this work offers, in outline, the general formulations that show how these two different kinds of representations for semantic structures can (potentially) be unified and also proposes three desiderata for testing, in brain dynamics, the mathematical equivalence between formal symbolic representations (and their transitions), and neuronal population codes (and their transitions). (shrink)

i) We show for each context-free language L that by considering each word of L as a structure in a natural way, one turns L into a finite union of classes which satisfy a finitary analog of the characteristic properties of complete universal first order classes of structures equipped with elementary embeddings. We show this to hold for a much larger class of languages which we call free local languages. ii) We define local languages, a class (...) of languages between free local and context-sensitive languages. Each local language L has a natural extension L ∞ to infinite words, and we prove a series of "pumping lemmas", analogs for each local language L of the "uvxyz theorem" of context free languages: they relate the existence of large words in L or L ∞ to the existence of infinite "progressions" of words included in L, and they imply the decidability of various questions about L or L ∞ . iii) We show that the pumping lemmas of ii) are independent from strong axioms, ranging from Peano arithmetic to ZF + Mahlo cardinals. We hope that these results are useful for a model-theoretic approach to the theory of formal languages. (shrink)

Any discussion of the concept of “formal science” must acknowledge that the term is used in different ways, for different purposes, by different people. For some, the formal sciences are defined by the exclusive use of deductive methods for discovering, or reasoning about, the properties of formal, abstract systems. On this view, the formal sciences are synonymous with mathematics, formal logic, and certain branches of linguistics and computer science that emphasize the study of (...) class='Hi'>formal languages. For others, “formal science” means something like “exact science”, or “formalized science”. On this view, any scientific discipline that places heavy emphasis on mathematical or logical formalization of key theoretical concepts and theories, could be described as a formal science. This latter conception of formal science is much more liberal than the former, and would include all of physics, much of chemistry, and some parts of biology, ecology, psychology and economics, as well as newer computationoriented disciplines like artificial life and artificial intelligence that do not fit easily within the traditional classification of the sciences. (shrink)

Some algebraic structures of the set of all effects are investigated and summarized in the notion of a(weak) orthoalgebra. It is shown that these structures can be embedded in a natural way in lattices, via the so-calledMacNeille completion. These structures serve as a model ofparaconsistent quantum logic, orthologic, andorthomodular quantum logic.

Abstract The purpose of this paper is twofold: (i) we will argue that formal semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts, namely ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of, and relations between, objects of various ontological types; and (ii) we show that accounting for these differences amounts to a new formal semantics; one that (...) integrates lexical and compositional semantics in one coherent framework and one where formal semantics is embedded with a strongly typed ontology; an ontology that reflects our commonsense knowledge of the world and the way we talk about it in ordinary language. We will show how in such a framework a number of challenges in the semantics of natural language are adequately and systematically treated. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results (...) hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

Arbitrary symbolism is a linguistic doctrine that predicts an orthogonal relationship between word forms and their corresponding meanings. Recent corpora analyses have demonstrated violations of arbitrary symbolism with respect to concreteness, a variable characterizing the sensorimotor salience of a word. In addition to qualitative semantic differences, abstract and concrete words are also marked by distinct morphophonological structures such as length and morphological complexity. Native English speakers show sensitivity to these markers in tasks such as auditory word recognition and naming. One (...) unanswered question is whether this violation of arbitrariness reflects an idiosyncratic property of the English lexicon or whether word concreteness is a marked phenomenon across other natural languages. We isolated concrete and abstract English nouns, and translated each into Russian, Arabic, Dutch, Mandarin, Hindi, Korean, Hebrew, and American Sign Language. We conducted offline acoustic analyses of abstract and concrete word length discrepancies across languages. In a separate experiment, native English speakers with no prior knowledge of these foreign languages judged concreteness of these nouns. Each naïve participant heard pre-recorded words presented in randomized blocks of three foreign languages following a brief listening exposure to a narrative sample from each respective language. Concrete and abstract words differed by length across five of eight languages, and prediction accuracy exceeded chance for four of eight languages. These results suggest that word concreteness is a marked phenomenon across several of the world's most widely spoken languages. We interpret these findings as supportive of an adaptive cognitive heuristic that allows listeners to exploit non-arbitrary mappings of word form to word meaning. (shrink)

The essays in this collection are the outgrowth of a workshop, held in June 1976, on formal approaches to the semantics and pragmatics of natural languages. They document in an astoundingly uniform way the develop ments in the formal analysis of natural languages since the late sixties. The avowed aim of the' workshop was in fact to assess the progress made in the application of formal methods to semantics, to confront different approaches to essentially the (...) same problems on the one hand, and, on the other, to show the way in relating semantic and pragmatic explanations of linguistic phenomena. Several of these papers can in fact be regarded as attempts to close the 'semiotic circle' by bringing together the syntactic, semantic and pragmatic properties of certain constructions in an explanatory framework thereby making it more than obvious that these three components of an integrated linguistic theory cannot be as neatly separated as one would have liked to believe. In other words, not only can we not elaborate a syntactic description of (a fragment of) a language and then proceed to the semantics (as Montague pointed out already forcefully in 1968), we cannot hope to achieve an adequate integrated syntax and semantics without paying heed to the pragmatic aspects of the constructions involved. The behavior of polarity items, 'quantifiers' like any, conditionals or even logical particles like and and or in non-indicative sentences is clear-cut evidence for the need to let each component of the grammar inform the other. (shrink)

Atomic propositions and their properties are the core of the philosophy of language. To define atomic propositions, it is necessary to clarify their nature. To this end, Frege, Russell, and Wittgenstein tried to understand the nature of atomic propositions by examining their unity. The question of the unity of atomic propositions has not been uniformly resolved, however. Frege and Russell largely agreed on the category and role of propositions, thinking that the object represented by a proposition is a Platonic (...) abstract entity, but they had different understandings of the unity of propositions. Wittgenstein took a different approach, holding that the object of a proposition representation is the linguistic picture entity. Based on this understanding, the problem of examining the unity of atomic propositions becomes the problem of examining the representation form and content of the proposition, thus avoiding the formal ontology of propositions. Atomic propositions are the basic unit formed by the cognitive subject in the activity of representing the world, and their nature is the unity of the transcendental intentionality of the cognitive subject and the experiential activity. (shrink)

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language‐learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners’ input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized learning biases. The test case is an experiment (Culbertson, Smolensky, & Legendre, 2012) targeting the learning of word‐order patterns in the nominal domain. The model identifies internal biases of (...) the experimental participants, providing evidence that learners impose (possibly arbitrary) properties on the grammars they learn, potentially resulting in the cross‐linguistic regularities known as typological universals. Learners exposed to mixtures of artificial grammars tended to shift those mixtures in certain ways rather than others; the model reveals how learners’ inferences are systematically affected by specific prior biases. These biases are in line with a typological generalization—Greenberg's Universal 18—which bans a particular word‐order pattern relating nouns, adjectives, and numerals. (shrink)

This paper articulates a formal theory of belief incorporating three key theses: (1) belief is a dyadic relation between an agent and a property; (2) this property is not the belief's truth condition (i.e., the intuitively self-ascribed property which the agent must exemplify for the belief to be true) but is instead a certain abstract property (a "thought-content") which contains a way of thinking of that truth condition; (3) for an agent a to have a belief "about" such-and-such items (...) it is necessary that a possesses a language of thought, $M_{a}$ , and that a (is disposed as one who) inwardly affirms a sentence of $M_{a}$ in which there are terms that denote those objects. Employing an extended version of E. Zalta's system ILAO, the proffered theory locates thought-contents within a typed hierarchy of "senses" and their "modes of presentation", the provisional definitions of which (suppressing complications added later to accommodate the contents of beliefs about beliefs) are as follows. A mode of presentation of e is a ternary relation of the sort [λxyz z is a name in $M_{y}$ that denotes x, and $D_{e}yz$ ] in which $D_{e}$ is an e-determiner - a relation between agents and their mental expressions imposing a syntactico-semantic condition sufficient for such an expression to denote e therein. A sense of an entity e is an abstract property that "contains" a mode of presentation $R_{e}$ of e by dint of encoding its property-reduct [λx(∃y)(∃z) $R_{e}xyz$ ]. In particular, a thought-content is a sense T of an ordinary first-order property P containing a mode of presentation whose P-determiner $D_{P}$ is such that, for any y and z, $D_{P}yz$ entails that z is a λ-abstract [λv S] of $M_{y}$ in which S is a sentence whose non-logical parts stand in appropriate semantic relations to the constituents of T's (some of which may themselves be senses). Where $I_{a}$ is agent a's dedicated self-demonstrative and |T| is the mode of presentation contained in a thought-content T, the belief relation itself is then characterized as obtaining between a and T iff a( is disposed as one who) inwardly affirms the substitution instance $S(I_{a}/v)$ of a sentence S in $M_{a}$ such that |T|(P, a, [λv S]). The aforementioned "constituents" and "appropriate semantic relations" are formally characterized so as to permit a system of canonical descriptions for thought-contents of arbitrary complexity. These canonical descriptions are then employed to chart the nature and interrelations of belief de re, de dicto and de se and to identify the source of opacity in belief ascription. (shrink)

The paper examines the invariance principles proposed by the analytical and phenomenological traditions for demarcating the boundaries of formal and regional ontologies. The principle of invariance with respect to isomorphic transformations, generalizing Alfred Tarski’s criterion for logical concepts, is extended to formal ontology as the theory of manifolds in its phenomenological interpretation. Isomorphism types, which are abstract individuals of the highest order, hypostases of forms of all possible ontologies, are considered as model-theoretical analogs of manifolds. The correlativity of (...) the phenomenological principles of demarcation of ontological regions and the criterion of invariance with respect to isomorphic transformations is demonstrated, leading to the convergence of logic and formal mathematics in both traditions and, at the same time, to the exclusion of geometry from formal ontology. Particular attention is paid to the discussion of the analytical and phenomenological traditions of the synthetic (material) a priori and the contribution that Wittgenstein’s doctrine on internal relations at different stages of its evolution makes to this discussion. The paper reveals the basis for later Wittgenstein’s criticism of his earlier project of creating a phenomenological language for expressing internal regional relations (such as the colours exclusion). The paper shows how Wittgenstein’s doubts about the possibility of an ideal notation based on the dichotomy of the logical and phenomenological led him to the study of invariants arising in language games. These invariants are not determined by the special properties of the categorical objects of formal ontology or the structures of regional subject matter, but are stable equilibria generated by the “consensus of actions.” New perspectives are outlined that are opened for logic and phenomenology by switching focus from the invariants of ontological structures to the invariants of structured interactions of various agents. (shrink)

In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.

Sweet describes the pragmatic foundations of standard logic and applies these foundations to the task of developing a theory of intended models as an extension of standard model theory in which the relevant "intending" is represented pragmatically. Methods of formal logic are used to investigate the structure of the relation between language and the world. The truism which holds that this relation includes the speaker as well as the object spoken about is formally explicated and applied to the problem (...) of illuminating one of the deepest phenomena in standard model theory: the existence of non-isomorphic models of complete theories. To this end it is shown that standard logic admits pragmatic foundations upon which a theory of intended models can be built as an extension of standard model theory. The relevant "intending" is represented by the very forms of verbal behavior which determine the grammatical and logical structure of the sentences whose referential meaning is in question. The uniqueness properties of the class of intended models may then be described. The first section of the book states the immediate goal of standard pragmatics as that of recovering the algebraic structure first-order logic by means of a purely pragmatic construction. The second section, the major portion of the work, then provides the foundation for a semiotic theory of intended models and referential meaning. The theory is then applied to the problem of referential indeterminancy, which has been associated with the phenomenon of scientific revolutions. The theory is also applied to the problem of the apparent synonymy of observationally equivalent theories. Sweet concludes that such theories are not referentially synonymous in any natural sense which is analogous to the paradigm sense in which theories of alternative scales of measurement are referentially synonymous. A novel feature of this book is the formal explication of the idea that the factors, pragmatical in nature, which distinguish the actual meaning of a sentence from among its possible meanings, whose range is defined by the manner in which the sentence is parsed, determine that very parsing. Applicability to natural language of the model-theoretic semantics thereby obtained is made possible by another feature of the book: the development of a theory of locally standard grammar which provides the foundation for representing the structure of natural language as that of standard first-order logic, in a local, as distinguished from a global, sense. This book is intended for scholars in logic, semiotics, and the philosophies of language and of science. Those concerned specifically with such philosophers as Peirce, Martin, and Davidson will also find the study valuable. (shrink)

The article approaches cut elimination from a new angle. On the basis of an arbitrary inference relation among logically atomic formulae, an inference relation on a language possessing logical operators is defined by means of inductive clauses similar to the operator-introducing rules of a cut-free intuitionistic sequent calculus. The logical terminology of the richer language is not uniquely specified, but assumed to satisfy certain conditions of a general nature, allowing for, but not requiring, the existence of infinite conjunctions and disjunctions. (...) We investigate to what extent structural properties of the given atomic relation are preserved through the extension to the full language. While closure under the Cut rule narrowly construed is not in general thus preserved, two properties jointly amounting to closure under the ordinary structural rules, including Cut, are. -/- Attention is then narrowed down to the special case of a standard first-order language, where a similar result is obtained also for closure under substitution of terms for individual parameters. Taken together, the three preservation results imply the familiar cut-elimination theorem for pure first-order intuitionistic sequent calculus. -/- In the interest of conceptual economy, all deducibility relations are specified purely inductively, rather than in terms of the existence of formal proofs of any kind. (shrink)

This paper examines from a special perspective the problem of methodological limita­tions of the computational approach in the philosophy of mind and empirical sciences. The main goal is to consistently substantiate the dependence of philosophical “metaphori­cal dictionaries” on advances in the field of computer science, historical contexts of epis­temology, formal and methodological limitations of algorithmic and computational proce­dures. The key idea is that despite the success of computational models in empirical re­search, their conceptual level does not allow us to (...) correctly formulate the question of the ontology of consciousness. Computationalism in philosophical theories of con­sciousness is presented as a practice of word usage, which posits systems of consistent descriptions of the information properties of consciousness and cognitive processes within the framework of certain methodological rules. The limitations of the computa­tional approach are associated with the lack of a scientific theory of subjectivity, the fun­damental irreducibility of external properties of consciousness to internal states, and fun­damental restrictions on the completeness and consistency of computer mathematics. A classification of several anti-computational programs has been carried out. The article discusses various limitations of computational approaches, such as: the complexity of for­malizing nonlinear and hidden processes, the dependence of emotions and intuition on the situational context and individual differences, the difficulty of predicting the emerg­ing properties of autonomous and autopoietic systems, and the limitations associated with non-standard computational processes of quantum and dynamic phenomena. A special role is given to the problem of set-theoretic reductive realism within the framework of mathe­matical structuralism and some aspects of p-adic number systems as a possible alternative to a “universal language” for the computational philosophy of consciousness. (shrink)

The van Wijngaarden grammars are two-level grammars that present many interesting properties. In the present article I elaborate on six of these properties, to wit, (i) their being constituted by two grammars, (ii) their ability to generate (possibly infinitely many) strict languages and their own metalanguage, (iii) their context-sensitivity, (iv) their high descriptive power, (v) their productivity, or the ability to generate an infinite number of production rules, and (vi) their equivalence with the unrestricted, or Type-0, Chomsky (...) grammars. (shrink)

Some formal properties of enriched systems of Lambek calculus with analogues of conjunction and disjunction are investigated. In particular, it is proved that the class of languages recognizable by the Lambek calculus with added intersective conjunction properly includes the class of finite intersections of context-free languages.

The traditional view is that 'now’ is a pure indexical, denoting the utterance time. Yet, despite its initial appeal, the view has faced criticism. A range of data reveal 'now’ allows for discourse-bound (i.e., anaphoric) uses, and can occur felicitously with the past tense. The reaction to this has typically been to treat ‘now’ as akin to a true demonstrative, selecting the prominent time supplied by the non-linguistic context or prior discourse. We argue this is doubly mistaken. The first mistake (...) concerns the semantic value of ‘now’, which is not a time, but a state — the consequent state of a prominent event. The second is that ‘now’ is a pure indexical after all, insofar as its interpretation is determined without recourse to extra-linguistic supplementation. Specifically, we argue that any occurrence of 'now’ selects the consequent state of the most prominent event, where event-prominence is linguistically maintained through prominence-affecting updates contributed by coherence relations. Our analysis accounts straightforwardly for a wide range of discourse initial and discourse bound uses of ‘now’, while giving it a simple indexical meaning. (shrink)

. The deep structural properties of a quantum information theoretic approach to formal languages and universal computation, as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.

Information is a peculiar quantity. Unlike matter and energy, which are conserved by the laws of physics, the aggregation of knowledge from many sources can in fact produce more information (synergy) or less (redundancy) than the sum of its parts. This feature can endow groups with problem‐solving strategies that are superior to those possible among noninteracting individuals and, in turn, may provide a selection drive toward collective cooperation and coordination. Here we explore the formal properties of information aggregation (...) as a general principle for explaining features of social organization. We quantify information in terms of the general formalism of information theory, which also prescribes the rules of how different pieces of evidence inform the solution of a given problem. We then show how several canonical examples of collective cognition and coordination can be understood through principles of minimization of uncertainty (maximization of predictability) under information pooling over many individuals. We discuss in some detail how collective coordination in swarms, markets, natural language processing, and collaborative filtering may be guided by the optimal aggregation of information in social collectives. We also identify circumstances when these processes fail, leading, for example, to inefficient markets. The contrast to approaches to understand coordination and collaboration via decision and game theory is also briefly discussed. (shrink)

Traditionally, analytic philosophy has been affiliated with a formalist conception of inference which understands reasoning as a process that exploits syntactic properties of natural language according to a set of formal rules that are insensitive to conceptual content. This chapter discusses an alternative approach that takes semantic properties as the underlying forces driving rational inference. Building on Wilfird Sellars’ notion of material inference and analytic tools from cognitive linguistics, I will show how parts of the inferential structure (...) of natural language can be explained in terms of semantic relations between extra-logical concepts. In the end, I will outline a strategy for explicating some of these inference-types using Peter Gärdenfors’ theory of conceptual spaces. (shrink)

We present an axiomatic framework for semantics that can be applied to natural and formal languages. Our main goal is to suggest a very simple mathematical model that describes fundamental cognitive aspects of the human brain and that can still be applied to artificial intelligence. One of our main results is a theorem that allows us to infer syntactical properties of a language out of its corresponding semantics. The role of pragmatics in semantics in our mathematical framework (...) is also discussed. (shrink)

Language employs various coordinators to connect propositions, a subset of which are “logical” in nature and thus analogous to the truth operators of formal logic. We here focus on two linguistic connectives and their negations: conjunction _and_ and (inclusive) disjunction _or_. Linguistic connectives exhibit a truth-conditional component as part of their meaning (their semantics), but their use in context can give rise to various implicatures and presuppositions (the domain of pragmatics) as well as to inferences that go beyond semantic/pragmatic (...) properties (the result of reasoning processes). We provide a comprehensive review of the role of the logical connectives in language and argue that three sets of factors—semantic, pragmatic, and those related to reasoning—are separate and separable, though some details may differ cross-linguistically. As a way to showcase the argument, we present two experiments in language comprehension in Spanish wherein pragmatic content was minimised and reasoning processes neutered, thus potentially highlighting what might be the default meanings of the connectives under study. In Experiment 1 we show that the conjunctive reading of inclusive disjunction is available in positive contexts other than in syntactically intricate cases such as downward entailing and free choice contexts, contrary to what has been claimed in the literature. In Experiment 2 we show that negated conjunctions and disjunctions in Spanish can easily receive the same interpretation when contrasted against the same context and, moreover, that these interpretations match those available in English, despite claims from the literature that linguistic connectives and local negation interact differently in English and Romance languages. (shrink)