Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb's stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle (...) of maximum entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state - such as a plausibility ranking over hypotheses, or a belief set - the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generated AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of beliefs. (shrink)

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)

Given current data, only a few binary Boolean operators are expressed in lexically simple fashion in the world's languages: and, or, nor. These do not occur in every combination, for example, nor is not observed by itself. To explain these cross‐linguistic patterns, we propose an encoding of Boolean operators as update procedures to accept or reject information in a context. We define a measure of conceptual simplicity for such updates, on which attested operators are conceptually simpler than (...) the remaining Booleans. Moreover, we show that language evolution selects for the attested lexical inventories by minimizing the complexity of using a lexical inventory compositionally to convey precise information. (shrink)

This essay argues that there are theoretical benefits to keeping distinct—more pervasively than the literature has done so far—the psychological states of imagining that p versus believing that in-the-story p, when it comes to cognition of fiction and other forms of narrative. Positing both in the minds of a story’s audience helps explain the full range of reactions characteristic of story consumption. This distinction also has interesting conceptual and explanatory dimensions that haven’t been carefully observed, and the two mental state (...) types make distinct contributions to generating emotional responses to stories. Finally, the differences between the mental states illuminate how a given story can be both shared with others and at the same time experienced as personal. (shrink)

Cappelen and Hawthorne’s Relativism and Monadic Truth (2009) offers an extended defense of a thesis they call simplicity, which, in brief, holds that propositions are true or false simpliciter. Propositions are cast in their traditional roles as the contents of assertions, and as the semantic values of declarative sentences in contexts. Simplicity stands in sharp contrast to forms of relativism including, for instance, a form that hold that our claims are true or false only relative to a judge. This applies (...) especially to claims of taste, which come out true or false only relative to the judge who finds things tasty (e.g. Glanzberg 2007, Lasersohn 2005). But simplicity also rejects the more widespread temporalist view that propositions are true or false only relative to a time, and it rejects the even more widely held view that propositions are true or false only relative to a world. One reason that has been advanced for temporalism, e.g. by Kaplan (1989), is that our languages seem to contain non-trivial temporal operators. Hence, the argument goes, the semantic values of sentences need to be temporally neutral, i.e. vary for truth or falsehood with time. The same goes for possible worlds and modal operators. Hence, Kaplan and many others think of the semantic values of sentences as sets of world-time pairs. It has been tempting to apply this sort of argument much more widely, to see the semantic values of sentences as varying not just with world and time, but perhaps with location and other parameters as well. Kaplan.. (shrink)

Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining (...) truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics. (shrink)

Ewald considered tense operators G, H, F and P on intuitionistic propositional calculus and constructed an intuitionistic tense logic system called IKt. In 2014, Figallo and Pelaitay introduced the variety IKt of IKt-algebras and proved that the IKt system has IKt-algebras as algebraic counterpart. In this paper, we introduce and study the variety of tense Nelson algebras. First, we give some examples and we prove some properties. Next, we associate an IKt-algebra to each tense Nelson algebras. This result allowed (...) us to determine the congruence of the tense Nelson algebras and also to characterize the subdirectly irreducible tense Nelson algebras and particularly the simple tense Nelson algebras. Finally, we prove that there exists an equivalence between the category of IKt-algebras and the category of tense centered Nelson algebras. (shrink)

Any language $$\mathcal {L}$$ L of classical logic, of first- or higher-order, is expanded with sentential quantifiers and operators. The resulting language $$\mathcal {L}^+\!$$ L +, capable of self-reference without arithmetic or syntax encoding, can serve as its own metalanguage. The syntax of $$\mathcal {L}^+$$ L + is represented by directed graphs, and its semantics, which coincides with the classical one on $$\mathcal {L}$$ L, uses the graph-theoretic concepts of kernels and semikernels. Kernels provide an explosive semantics, while semikernels (...) generalize this to situations where paradoxes do not lead to explosion, thus distinguishing them from contradictions. Paradoxes arise only at the metalevel due to specific interpretations of the operators, but they can be avoided: $$\mathcal {L}^+$$ L + can express paradoxes but remains free from them. For an expansion $$\mathcal {L}^+$$ L + of any FOL language $$\mathcal {L}$$ L, with the non-explosive semantics, a complete reasoning system is obtained by extending Gentzen’s classical sequent calculus with two rules for the sentential quantifiers. Adding (cut) yields a complete system for the explosive semantics. The novel semantics and self-referential capabilities seem promising for a further extension of classical logic towards one capable also of consistently expressing its own syntax and truth theory. (shrink)

The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative (...) extensions of K, using a novel generalisation of the standard semantics. (shrink)

We give $A_p$ type conditions which are sufficient for two-weight, strong $$ inequalities for Calderón-Zygmund operators, commutators, and the Littlewood-Paley square function $g^*_\lambda $. Our results extend earlier work on weak $$ inequalities in [13].

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.

A philosophical discussion of the intuitive meaning of the formalism of modal propositional logics.

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some point (...) on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

Following the idea of L -fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L -fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L -fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L -fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an (...) order isomorphic mapping between upper and lower approximation operators based on L -fuzzy generalized neighborhood systems; when L -fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L -fuzzy relations are complete lattice isomorphism. (shrink)

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often (...) justified only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

Since the turn of the century, the number of small-scale farmers in the U.S. and farmlands they owned have declined very sharply (structural change). Although the decrease in number is generally true for both white and Black farm operators, it has been more significant for Blackfarm operators than whites. The declining trend in the number of Blackfarm operators in the country is derived from individual state experiences that resulted from a combination of various political and economic factors. (...) Using the census of agriculture data from 1900 to 1987, this paper gives a brief historical overview of Black farm operators in Maryland. The census data for the study period shows that at their peak number in 1910, there were 6,382 Blackfarmers in the state of Maryland. However, by 1987, only 371 of that number remained, representing a loss of 94 percent since 1910. According to the 1987 census data almost all Black operated farms in Maryland were not only small-scale but also in the lower sales class, less than $20,000 a year. Their household net family income is below that of non-metropolitan median household income. This concentration of Blacks in the lower economic class of farm operators in the state, for the most part, is closely related to their resource endowments, patterns of tenure, type of farm enterprises, and government farm programs and policies. On the average, Blackfarmers in Maryland have less land, capital and management skills than their white counterparts. Government policies and programs had, and continue to have, a devastating effect on Maryland Black farmers because they were tied to productive resources rather than farm income needs. Under conditions of low income, years of neglect by federal and state programs and policies, and limited resources Blackfarmers were unable to adopt capital intensive production practices and expand their farm operations. This resulted in most of them leaving agriculture, in the past and today, at a faster rate than whites. To avert or at least lessen the unfortunate situation of Black farm operators, projections and possible solutions are offered. This includes how the 1890 Land-Grant institutions because of their tradition, expertise and experience of research, teaching and outreach can take the leadership role in shaping the future direction of these farmers and their operations. (shrink)

This paper is devoted to the concepts of consequence and rejection, formulated as operators on a nonempty set of sentences, which may initially be unstructured. One of the issues that we pay attention to is the “cyclicity” of these concepts when they are defined one through the other. In addition, we explore this cyclicity, when the set of all sentences acquires some structure, or we can assume some structure of sentences in the sense that the operation of substitution can (...) be applied to them. (shrink)

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

Until recently most militaries tended to see moral issues through the lens of rules and regulations. Today, however, many armed forces consider teaching virtues to be an important complement to imposing rules and codes from above. A closer look reveals that it is mainly established military virtues such as honour, courage and loyalty that dominate both the lists of virtues and values of most militaries and the growing body of literature on military virtues. Although there is evidently still a role (...) for these traditional martial virtues, it is equally evident that they are not particularly relevant to, for instance, military personnel operating drones. This chapter looks into the ethics of unmanned warfare from the perspective of military virtues and military ethics education, and addresses the question of what we need to solve that just-mentioned misalignment: 1) a new set of virtues; 2) a different interpretation of the existing virtues; or 3) a different approach altogether, that is, an alternative to teaching virtues? That we have to think about such questions is at least partly because unmanned systems bring risk asymmetry in war to a new level, making warlike virtues such as physical courage by and large obsolete. The last section of this chapter therefore addresses the question: to what extent does the possibility of riskless warfare makes drone use ‘virtue-less’? (shrink)

In this paper I introduce and develop an approach to tenses and temporal expressions that is a mix between eternalism and temporalism consisting in appeal to ‘variadic operators’. The type of variadic operator I will be concerned with is the expansive variadic operator, which takes as input predicates of a certain adicity and yields new predicates with one additional degree of adicity. Appeal to variadic operators has proven useful in giving the semantics of several types of expressions: adverbs (...) ), prepositional phrases ), relational terms ), etc. The focus of this paper is on tenses and temporal expressions, with the aim of showing how these are treated by appeal to temporal variadic operators. First I define the temporal variadic operator and then show how it can be used to account for simple tensed sentences. I also give a rough sketch of how it can accommodate more complex phenomena like sequence of time, interaction between tenses and temporal adverbials, temporal anaphora, later-than-matrix and double-access readings, etc. (shrink)

We propose an extension of minimal intuitionistic predicate logic, based on delimited control operators, that can derive the predicate-logic version of the double-negation shift schema, while preserving the disjunction and existence properties.

The Embracing Revenge account of semantic paradox avoids the expressive limitations of previous approaches based on the Kripkean fixed point construction by replacing a single language with an indefinitely extensible sequence of languages, each of which contains the resources to fully characterize the semantics of the previous languages. In this paper we extend the account developed in Cook (2008), Cook (2009), Schlenker (2010), and Tourville and Cook (2016) via the addition of intensional operators such as ``is paradoxical''. In this (...) extended framework we are able to characterize the difference between sentences, such as the Liar and the Truth-teller, that receive the same semantic value in minimal fixed points yet seem to involve distinct semantic phenomena. (shrink)

Gamma rhythms are associated with external and internal sensory processing. Within the conceptual framework of “top-down” and “bottom-up” processing, this suggests that gamma represents a format common to both camps. As these oscillations facilitate communication in the temporal domain, they may represent a mechanism by which top-down and bottom-up processing can interact. A breakdown in this interaction may lead to hallucinations.

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of (...) general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. (shrink)

(No abstract is available for this citation).

We investigate the join semilattice of modal operators on a Boolean algebra B. Furthermore, we consider pairs ⟨f,g⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle f,g \rangle $$\end{document} of modal operators whose supremum is the unary discriminator on B, and study the associated bi-modal algebras.

The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics (...) that are sound and complete with respect to varieties of distributive lattices with operators in the above-mentioned classes. (shrink)

There are a considerable number of logics that do not seem to share the same inferential principles. Intuitionistic logics do not include the law of the exclude.

This is my contribution to a symposium on Berit Brogaard's book "Transient Truths" in which I criticize her treatment of various linguistic phenomena related to tense.

In this paper we consider the algebra of differential operators with polynomial coefficients acting on Clifford algebra-valued functions from both sides. We characterize the subalgebra of SO(m)-invariant differential operators, which itself contains the subalgebra of GL(m)-invariant differential operators.

The coordinate-free methods of the preceding paper are illustrated in three problems. First, the electrodynamics of a homogeneous, isotropic, and gyrotropic medium is investigated; it is shown that such a medium can exhibit optical activity, and the propagation of a plane electromagnetic wave in such a medium is discussed. Then, the electrodynamics of a homogeneous system made anisotropic by a uniform external magnetic field is considered; a description of Faraday rotation is provided, the ionosphere being used in an example. Finally, (...) the reflection and refraction of a plane electromagnetic wave at the interface of two media are described by coordinate-free operators. (shrink)

The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety (...) of the algerabic models of the given logics, soundness and completeness with respect to these classes of Kripke-style models follows by using entirely algebraical arguments from the soundness and completeness of the logic with respect to its algebraic models. (shrink)

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic _bringing it about that_. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction (...) to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules. (shrink)