This paper surveys important work done in relevant logic in the past 10 years.

I have three main objectives in this essay. First, in chapter 2, I shall put forward and justify what I call worldlessness, by which I mean the following: All truths (as well as falsehoods) are wholly independent of any circumstances, not only time and place but also possible worlds. It follows from this view that whatever is actually true must be taken as true with respect to every possible world, which means that all truths are (in a sense) necessary. However, (...) the account I shall propound is different from what is known in the trade as necessitarianism, i.e. the view that there is only one possible world, viz. the actual one, for the doctrine of the worldlessness of truth values, despite its commitment to the necessity of truths and falsehoods, is quite compatible with the idea of there being other possible worlds. Another important issue in chapter 2, explored in particular in section 2.12, is the claim that there is no real change in the world. Secondly, in chapter 3 I consider the eminent traditional argument for determinism, deriving from Aristotle, namely, logical determinism, i.e. determinism justified by an appeal to the logical principle of bivalence (that all proper statements, including those concerning the future, are either true or false). In this connection I try to show that, (i), the formulation of the conclusion of this argument as "Whatever will happen will happen of necessity" is implausible, at least from the modern point of view, (ii), the formulation as "Whatever will happen will happen inevitably" is more to the point, and (iii), on the basis of the worldless and timeless aspect advocated in chapter 2, this latter formulation is quite harmless, essentially amounting to the trivial statement, "Whatever will happen will happen". Thirdly, in chapter 4 I study theological determinism, or determinism that arises from God's supposed providential control over everything that happens. In this connection, I shall survey some historical accounts of the relation between human free will and determinism (not only theological but also causal determinism); the philosophers the views of whom I shall attend to include Chrysippus, St. Augustine, Boethius and Aquinas. I shall in particular consider G.W. Leibniz' theodicean aspirations, viz. his solution to the problem of evil and, especially, his compatibilist attempts to reconcile human free will with the strictly deterministic flow of actual events. I think it is important to try to explicate Leibniz' ingenious account of these matters, since it seems that it has not been fully appreciated in the literature, not even by contemporary Leibniz scholars (such as B. Mates, R.C. Sleigh, C. Wilson, R.M. Adams and D. Rutherford). In providing the Leibnizian compatibilist solution of the problem of determinism and freedom in chapter 4, I shall utilize the approach of chapter 2. (shrink)

Fine and Kripke extended S5, S4, S4.2 and such to produce propositionally quantified systems , , : given a Kripke frame, the quantifiers range over all the sets of possible worlds. is decidable and, as Fine and Kripke showed, many of the other systems are recursively isomorphic to second-order logic. In the present paper I consider the propositionally quantified system that arises from the topological semantics for S4, rather than from the Kripke semantics. The topological system, which I dub , (...) is strictly weaker than its Kripkean counterpart. I prove here that second-order arithmetic can be recursively embedded in . In the course of the investigation, I also sketch a proof of Fine's and Kripke's results that the Kripkean system is recursively isomorphic to second-order logic. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

It is commonly believed that the role of context cannot be ignored in the analysis of conditionals, and counterfactuals in particular. On truth conditional accounts involving possible worlds semantics, conditionals have been analysed as expressions of relative necessity: “If A, then B” is true at some world w if B is true at all the A-worlds deemed relevant to the evaluation of the conditional at w. A drawback of this approach is that for the evaluation of conditionals with the same (...) antecedents at some world, the same worlds are deemed as relevant for all occasions of utterance. But surely this is inadequate, if shifts of contexts between occasions are to be accounted for. Both the linguistic and logical implications of this defect are discussed, and in order to overcome it a modification of David Lewis’ ordering semantics for counterfactuals is developed for a modified language. I follow Lewis by letting contexts determine comparative similarity assignments, and show that the addition of syntactic context parameters (context indices) to the language gives the freedom required to switch between sets of relevant antecedent worlds from occasion to occasion by choosing the corresponding similarity assignment accordingly. Thus an account that extends Lewis’ analysis of a language containing a single counterfactual connective > to a language containing infinitely many counterfactual connectives >_c, each indexed by a different context name c, overcomes the limitations of traditional analyses. Finally it is also shown that these traditional accounts can be recovered from the modified account if certain contextual restrictions are in place. -/- . (shrink)

A common framing has it that any adequate treatment of quotation has to abandon one of the following three principles: (i) The quoted expression is a syntactic constituent of the quote phrase; (ii) If two expressions are derived by applying the same syntactic rule to a sequence of synonymous expressions, then they are synonymous; (iii) The language contains synonymous but distinct expressions. In the following, a formal syntax and semantics will be provided for a quotational language which adheres to all (...) three principles. The point here is not merely to provide a “possibility proof”, but to reveal the hard constraints on the theory of quotation, and to highlight certain assumptions at the syntax/semantics/post-semantics interfaces. (shrink)

This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of \, \ and \.

We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don’t know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic belief revision. The key idea we (...) exploit to achieve non-omniscience focuses on topic- or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. (shrink)

Possible worlds models of belief have difficulties accounting for unawareness, the inability to entertain (and hence believe) certain propositions. Accommodating unawareness is important for adequately modelling epistemic states, and representing the informational content to which agents have in principle access given their explicit beliefs. In this paper, I develop a model of explicit belief, awareness, and informational content, along with an sound and complete axiomatisation. I furthermore defend the model against the seminal impossibility result of Dekel, Lipman and Rustichini, according (...) to which three intuitive conditions preclude non-trivial unawareness on any possible worlds model of belief. (shrink)

ABSTRACT We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical views that (...) its predecessors rule out by fiat. (shrink)

This chapter provides a general overview of the issues surrounding so-called semantic monsters. In section 1, I outline the basics of Kaplan’s framework and spell out how and why the topic of “monsters” arises within that framework. In Section 2, I distinguish four notions of a monster that are discussed in the literature, and show why, although they can pull apart in different frameworks or with different assumptions, they all coincide within Kaplan’s framework. In Section 3, I discuss one notion (...) that has spun off into the linguistics literature, namely “indexical shift”. In Section 4, I emphasize the connection between monsters and the compositionality of asserted content in Kaplan’s original discussion. Section 5 discusses monsters and the more general idea of re-interpretation or meaning-shift. Section 6 closes with a brief survey of where monsters may dwell, and pointers to avenues for future research. (shrink)

We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...) theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play. (shrink)

Formal semantics constitutes the framework of this thesis, and the aim is to characterise the semantics of the progressive, as it appears in sentence. Max was running towards the station Among the problems is one known as the "imperfective paradox". According to intuitions, sentence entails, but no entailment holds between and. Max was running towards the station Max ran towards the station Max was running to the station Max ran to the station Since and would seem to have the same (...) logical form, they ought to have similar entailments. Why is this not so? This thesis is divided into two parts. The first part, containing chapters 2 to 5, evaluates the current formal theories that tackle the imperfective paradox. Solving the imperfective paradox consists of two tasks: the first is to characterise a semantic distinction between and, and the second is to supply a semantic analysis of the progressive that is sensitive to this distinction and so results in a solution to the imperfective paradox. According to how the current theories tackle these two tasks, they can be classified into three camps which I will name as follows: the Heterogeneous Strategy provides one approach for fulfilling the first task, the Eventual Outcome Strategy provides an approach for defining the semantics of the progressive, and the Event-based Strategy provides a further alternative for achieving the two tasks at hand. All these strategies are intuitively motivated, but we will argue that they are ultimately untenable. The Heterogeneous Strategy and the Event-based Strategy fail to mesh with the treatment of point adverbials such as "At 3pm", and the Eventual Outcome Strategy produces a definition of the progressive that is viciously circular. Thus although the current theories that tackle the imperfective paradox are highly intuitively motivated, we will ultimately show that the formulations of these intuitions give rise to conflicts and tensions when it comes to explaining the natural language data. The second part of the thesis, containing chapters 6 and 7, offers a new approach for tackling the imperfective paradox. This new approach invokes two tools; the interval-based temporal logic IQ, and Moens' event-based AI model of temporal reference. IQ is an interval-based temporal logic with several innovations. First, unlike the previous interval-based theories, IQ maintains a high level of homogeneity: an atomic sentence is true at an interval I only if it is true at all subintervals of I. Second, IQ offers a technique whereby temporal expressions can have representations that receive their semantic interpretation with respect to context. We use the roles of homogeneity and context in IQ to characterise the semantics of aspect, where the characterisation is based on Moens' model. This provides an arena in which to tackle the imperfective paradox anew. We explain the entailment between and, and at the same time explain why no entailment holds between and. Furthermore, we overcome the problems concerning the treatment of adverbials such as "At 3pm" that are encountered in the Heterogeneous Strategy and the Event-based Strategy, and, since we do not adopt the Eventual Outcome Strategy in defining the progressive, we overcome that strategy's problem of circularity. Hence our solution to the imperfective paradox will provide answers to the puzzles posed in the earlier chapters of the thesis. (shrink)

The relevance of any logical analysis lies in its ability to solve paradoxes and trace conceptual troubles back; with this respect, the task of epistemic logic is to handle paradoxes in connection with the concept of knowledge. Epistemic logic is currently introduced as the logical analysis of crucial concepts within epistemology, namely: knowledge, belief, truth, and justification. An alternative approach will be advanced here in order to enlighten such a discourse, as centred upon the word assertion and displayed in terms (...) of utterance. Insofar as epistemic modalities express some attitudes, the intentionality of discourse will be emphasized within an illocutionary modal logic. Two large views will range over the whole study: declarative and epistemic sentences have one and the same logic (assertion logic); the plurality of languages games doesn’t entail any logical pluralism. -/- La valeur d'une analyse logique réside dans sa capacité à résoudre des paradoxes et à comprendre l'origine de nos problèmes conceptuels ; à ce titre, le rôle d'une logique épistémique est de traiter des paradoxes liés au concept de connaissance. On présente généralement la logique épistémique comme une analyse logique de concepts centraux en épistémologie : connaissance, croyance, vérité, justification. Une autre approche sera proposée ici en vue de clarifier ce genre de discours, centrée sur la notion d'assertion et décrite en termes d'énonciation. Parce que les modalités épistémiques expriment des attitudes, c'est l'intentionnalité du discours qui sera mise en valeur dans le cadre d'une logique modale illocutoire. Deux thèses transversales parcourront l'ensemble du travail : les énoncés déclaratifs et épistémiques partagent la même logique (logique assertorique) ; la pluralité des jeux de langages n'implique pas un pluralisme logique. (shrink)

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space (...) models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly. (shrink)

There is a difference between the conditions in which one can felicitously use a ‘must’-claim like and those in which one can use the corresponding claim without the ‘must’, as in 'It must be raining out' versus 'It is raining out. It is difficult to pin down just what this difference amounts to. And it is difficult to account for this difference, since assertions of 'Must p' and assertions of p alone seem to have the same basic goal: namely, communicating (...) that p is true. In this paper I give a new account of the conversational role of ‘must’. I begin by arguing that a ‘must’-claim is felicitous only if there is a shared argument for the proposition it embeds. I then argue that this generalization, which I call Support, can explain the more familiar generalization that ‘must’-claims are felicitous only if the speaker’s evidence for them is in some sense indirect. Finally, I propose a pragmatic derivation of Support as a manner implicature. (shrink)

By creating certain marks on paper, or by making certain sounds-breathing past a moving tongue-or by articulation of hands and bodies, language users can give expression to their mental lives. With language we command, assert, query, emote, insult, and inspire. Language has meaning. This fact can be quite mystifying, yet a science of linguistic meaning-semantics-has emerged at the intersection of a variety of disciplines: philosophy, linguistics, computer science, and psychology. Semantics is the study of meaning. But what exactly is "meaning"? (...) What is the exact target of semantic theory? Much of the early work in natural language semantics was accompanied by extensive reflection on the aims of semantic theory, and the form a theory must take to meet those aims. But this meta-theoretical reflection has not kept pace with recent theoretical innovations. This volume re-addresses these questions concerning the foundations of natural language semantics in light of the current state-of-the-art in semantic theorising. (shrink)

Montague and Kaplan began a revolution in semantics, which promised to explain how a univocal expression could make distinct truth-conditional contributions in its various occurrences. The idea was to treat context as a parameter at which a sentence is semantically evaluated. But the revolution has stalled. One salient problem comes from recurring demonstratives: "He is tall and he is not tall". For the sentence to be true at a context, each occurrence of the demonstrative must make a different truth-conditional contribution. (...) But this difference cannot be accounted for by standard parameter sensitivity. Semanticists, consoled by the thought that this ambiguity would ultimately be needed anyhow to explain anaphora, have been too content to posit massive ambiguities in demonstrative pronouns. This article aims to revived the parameter revolution by showing how to treat demonstrative pronouns as univocal while providing an account of anaphora that doesn't end up re-introducing the ambiguity. (shrink)

Kaplan (1989) famously claimed that monsters--operators that shift the context--do not exist in English and "could not be added to it". Several recent theorists have pointed out a range of data that seem to refute Kaplan's claim, but others (most explicitly Stalnaker 2014) have offered a principled argument that monsters are impossible. This paper interprets and resolves the dispute. Contra appearances, this is no dry, technical matter: it cuts to the heart of a deep disagreement about the fundamental structure of (...) a semantic theory. We argue that: (i) the interesting notion of a monster is not an operator that shifts some formal parameter, but rather an operator that shifts parameters that play a certain theoretical role; (ii) one cannot determine whether a given semantic theory allows monsters simply by looking at the formal semantics; (iii) theories which forbid shifting the formal "context" parameter are perfectly compatible with the existence of monsters (in the interesting sense). We explain and defend these claims by contrasting two kinds of semantic theory--Kaplan's (1989) and Lewis's (1980). (shrink)

A common view relating compositional semantics and the objects of assertion holds the following: Sentences φ and ψ expresses the same proposition iff φ and ψ have the same modal profile. Following Dummett, Evans, and Lewis, Stanley argues that this view is fundamentally mistaken. According to Dummett, we must distinguish the semantic contribution a sentence makes to more complex expressions in which it occurs from its assertoric content. Stojnić insists that views which distinguish the roles of content and semantic value (...) must nevertheless ensure a tight connection between the two. But, she contends, there is a crucial disanalogy between the views that follow Lewis and the views that follow Dummett. Stanley’s Dummettian view is argued to contain a fatal flaw: On such views, there is no way to secure an appropriate connection between semantic value and a theoretically motivated notion of assertoric content. I will review the background issues from Dummett, Evans, Lewis, and Stanley, and provide a principled way of bridging the gap between semantic value and a theoretically motivated notion of assertoric content. (shrink)

The verb 'knows' is often taken to be context-sensitive in an interesting way. What 'knows' means seems to be sensitive to the epistemic features of the context, e.g. the epistemic standard in play, the set of relevant alternatives, etc. There are standard model-theoretic semantic frameworks which deal with both intensional operators and context-sensitive expressions. In this chapter, we provide a brief overview of the various moving parts of these frameworks, the roles of context and index, the need for double indexing, (...) and the relationship between semantic value and content. With the best version of the standard framework explicated we then return at the end to the treatment of ‘know’ as a context-sensitive intensional operator (contrasting it with an invariantist treatment). (shrink)

In contemporary natural languages semantics one will often see the use of special brackets to enclose a linguistic expression, e.g. ⟦carrot⟧. These brackets---so-called denotation brackets or semantic evaluation brackets---stand for a function that maps a linguistic expression to its "denotation" or semantic value (perhaps relative to a model or other parameters). Even though this notation has been used in one form or another since the early development of natural language semantics in the 1960s and 1970s, Montague himself didn't make use (...) of this notation in his series of groundbreaking papers on semantics. That raises the question: When was the ⟦.⟧-notation introduced to semantics? This note answers that question. (shrink)

A “conceptual spaces” approach is used to formalize Aristotle’s main intuitions about time and change, and other ideas about temporal points of view. That approach has been used in earlier studies about points of view. Properties of entities are represented by locations in multidimensional conceptual spaces; and concepts of entities are identified with subsets or regions of conceptual spaces. The dimensions of the spaces, called “determinables”, are qualities in a very general sense. A temporal element is introduced by adding a (...) time variable to state functions that map entities into conceptual spaces. That way, states may have some permanency or stability around time instances. Following Aristotle’s intuitions, changes and events will not be necessarily instant phenomena, instead they could be processual and interval dependent. Change is defined relatively to the interval during which the change is taking place. Time intervals themselves are taken to represent points of view. To have a point of view is to look at the world as it is in the selected interval. Many important concepts are relativized to intervals, for instance change, events, identity, ontology, potentiality, etc. The definition of points of view as intervals allows to compare points of view in relation to all these concepts. The conceptual space approach has an immediate semantic and structural character, but it is tempting to develop also logics to describe them. A formal language is introduced to show how this could be done. (shrink)

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a (...) quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. (shrink)

The paper sketches an analysis of the notion of a self-fulfilling belief in terms of doxastic modal logic. We point out a connection between self-fulfilling beliefs and Moore’s paradox. Then we look at self-fulfilling beliefs in the context of neighborhood semantics. We argue that the analysis of several interesting self-fulfilling beliefs has to make essential use of propositional quantification.

Formal semantics and pragmatics as they have developed since the late 1960's have been shaped by fruitful interdisciplinary collaboration among linguists, philosophers, and logicians, among others, and in turn have had noticeable effects on developments in syntax, philosophy of language, computational linguistics, and cognitive science.In this paper I describe the environment in which formal semantics was born and took root, highlighting the differences in ways of thinking about natural language semantics in linguistics and in philosophy and logic. With Montague as (...) a central but not solo player in the story, I reflect on crucial developments in the 1960's and 70's in linguistics and philosophy, and the growth of formal semantics and formal pragmatics from there. I discuss innovations, key players, and leading ideas that shaped the development of formal semantics and its relation to syntax, to pragmatics, and to the philosophy of language in its early years, and some central aspects of its early impact on those fields. (shrink)

The truth-condition theory of meaning is, naturally, thought of an as explanatory theory whose explananda are the meaning facts. But there are at least two deductive arguments that purport to establish the truth of the theory irrespective of its explanatory virtues. This paper examines those arguments and concludes that they succeed.

When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly (...) for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A. (shrink)

Kaplan claims in Demonstratives that no operator may manipulate the context of evaluation of natural language indexicals. We show that this is not so. In fact, attitude reports always manipulate a context parameter (or, rather, a context variable). This is shown by (i) the existence of De Se readings of attitude reports in English (which Kaplan has no account for), and (ii) the existence of a variety of indexicals across languages whose point of evaluation can be shifted, but only in (...) attitude reports. We develop an alternative account within an extensional framework with overt quantification over times, worlds and contexts. Various typological facts are discussed, esp. the distinction between English, Amharic and Ewe pronouns, and that between English and Russian tenses. (shrink)

This paper contains an axiomatic theory of first order modal logic with operations, identity, and descriptions together with a formal semantics which interprets the theory in such a manner that empty universes of discourse and denotationless terms are allowed for at each possible world. The intuitive basis of the theory is discussed in preliminary sections, the syntax and semantics of theory are then characterized, its semantical adequacy is demonstrated, and certain important axioms and theorems are discussed in detail in later (...) sections. (shrink)

This papers gives a survey of recent results about simulations of one class of modal logics by another class and of the transfer of properties of modal logics under extensions of the underlying modal language. We discuss: the transfer from normal polymodal logics to their fusions, the transfer from normal modal logics to their extensions by adding the universal modality, and the transfer from normal monomodal logics to minimal tense extensions. Likewise, we discuss simulations of normal polymodal logics by normal (...) monomodal logics, of nominals and the difference operator by normal operators, of monotonic monomodal logics by normal bimodal logics, of polyadic normal modal logics by polymodal normal modal logics, and of intuitionistic modal logics by normal bimodal logics. (shrink)

This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the (...) Routley-Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable. (shrink)

The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A ∧ B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified (...) semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski. (shrink)

The paper studies first order extensions of classical systems of modal logic (see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown that these formulas correspond to fundamental properties of neighborhood frames. The results have interesting applications in epistemic logic. In particular we suggest that the proposed models can be used in order to study monadic operators of probability (Kyburg, 1990) and likelihood (Halpern-Rabin, 1987).

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)

Many philosophers are convinced that rationality dictates that one’s overall set of intentions be consistent. The starting point and inspiration for our study is Bratman’s planning theory of intentions. According to this theory, one needs to appeal to the fulfilment of characteristic planning roles to justify norms that apply to our intentions. Our main objective is to demonstrate that one can be rational despite having mutually inconsistent intentions. Conversely, it is also shown that one can be irrational despite having a (...) consistent overall set of intentions. To overcome this paradox, we argue that it is essential for a successful planning system that one’s intentions are practically consistent rather than being consistent or applying an aggregation procedure. Our arguments suggest that a new type of norm is needed: whereas the consistency requirement focuses on rendering the contents of one’s intentions consistent, our new practical consistency requirement demands that one’s intentions be able to simultaneously and unconditionally guide one’s action. We observe that for intentions that conform to the ‘own-action condition’, the practical consistency requirement is equivalent to the traditional consistency requirement. This implies that the consistency requirement only needs to be amended in scenarios of choice under uncertainty. (shrink)