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The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition's truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a unique value. In this paper we will study which modal logics can be obtained by changing the interpretation of the □ modality, assuming that the interpretation of other connectives stays constant. We will show what axioms are responsible for a particular interpretations of □ . Furthermore, we will study subsets of these axioms. We show that some of the combinations of the axioms are equivalent to well-known modal axioms. We apply the level-valuation technique to all of the systems to regain the closure under the rule of necessitation. We also point out that some of the resulting logics are not sublogics of S5 and comment briefly on the corresponding frame conditions that are forced by these axioms. Ultimately, we sketch a proof of meta-completeness for all of these systems. [ABSTRACT FROM AUTHOR]

This study argues that many of the formalizations used in analyses employing the notion of logical scope fail to conform to natural language in important ways and lead to false predictions. This is due to the fact that they pursue the logic-driven goal of making the structure of logical arguments more transparent and mechanically calculable rather than the language-driven goal of accounting for how the linguistic signs used in an utterance and their configuration contribute to the conveying of the message being fashioned by the speaker. The focus of the study is on categories associated with the verb: tense, aspect, modality and negation. The conclusion suggests that very precise and rigid theories using logical scope relations may force the theorist to straitjacket the data so that they fit the theory, thereby obscuring rather than clarifying the nature of linguistic categories and their interactions. Informal analyses that hew closer to natural language's semantic reality can provide greater understanding of phenomena such as the purported non-negatability of must. Seeing this English modal's meaning as defined in opposition to real existence leads to the realization that it does not interact with negation the same way as the reality of the existence of the property of being necessary does. [ABSTRACT FROM AUTHOR]

Putting individual constants and quantifiers into the same syntactic category within first-order language promises to have far-reaching consequences: a syntax of this kind can reveal the potential of any such language, allowing us to realize that a vast class of noun phrases, including non-denoting terms, can be accommodated in the new syntax as expressions suited to being subjects of sentences. In the light of this, a formal system that is an extension of classical first-order logic is developed here, and is equipped with an appropriate semantics. An ontological interpretation of the new logic is then also provided, with several categories of object and notions of existence being distinguished. Last but not least, a modal version of the logic, with some interesting formal features, is proposed. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain a Jónsson-style canonicity proof for the Sahlqvist fragment of distributive modal |$\mu $| -calculus in clopen semantics, alternative to the canonicity-via-correspondence argument in Conradie and Craig (2017, Journal of Logic and Computation , 27, 705–748), generalizing the results in Bezhanishvili and Hodkinson (2012, Theoretical Computer Science , 424, 1–19). The key ingredient of this proof is a characterization result about |$\sigma $| -contracting maps. [ABSTRACT FROM AUTHOR]

This article aims at providing some extension of the modal square of opposition in the light of Ockham's account of modal operators. Moreover, we set forth some significant remarks on the de re–de dicto distinction and on the modal operator of contingency by means of a set-theoretic algebra called numbering semantics. This generalization starting from Ockham's account of modalities will allow us to take into consideration whether Ockham's account holds water or not, and in which case it should be changed. [ABSTRACT FROM AUTHOR]

In this paper we present an extension of (bunched) separation logic, Boolean BI, with epistemic and dynamic epistemic modalities. This logic, called action model separation logic (AMSL ), can be seen as a generalization of public announcement separation logic in which we replace public announcements with action models. Then we not only model public information change (public announcements) but also non-public forms of information change, such as private announcements. In this context the semantics for the connectives ∗ and - ∗ from separation logic are epistemic versions of their usual semantics. This is because formulas are interpreted in states, not in resources, and agents may be uncertain between different states representing the same resource. We present the logic AMSL and its semantics, with a detailed case study that highlights its interest for modeling. We also prove the elimination of the dynamics modalities and discuss some alternative epistemic semantics for the separation connectives. [ABSTRACT FROM AUTHOR]

The paraconsistent and paracomplete 4-valued logic PŁ4 is originally interpreted with a two-valued Belnap-Dunn semantics. In the present paper, PŁ4 is endowed with both a ternary Routley-Meyer semantics and a binary Routley semantics together with their respective restriction to the 2 set-up case. [ABSTRACT FROM AUTHOR]

This work presents a proof-theoretical and model-theoretical approach to probabilistic temporal logic. We present two novel logics; each of them extends both the language of linear time logic (LTL) and the language of probabilistic logic with polynomial weight formulas. The first logic is designed for reasoning about probabilities of temporal events, allowing statements like "the probability that A will hold in next moment is at least the probability that B will always hold" and conditional probability statements like "probability that A will always hold, given that B holds, is at least one half", where A and B are arbitrary statements. We axiomatize this logic, provide corresponding sigma additive semantics and prove that the axiomatization is sound and strongly complete. We show that the satisfiability problem for our logic is decidable, by presenting a procedure which runs in polynomial space. We also present a logic with much richer language, in which probabilities are not attached only to temporal events, but the language allows arbitrary nesting of probability and temporal operators, allowing statements like "probability that tomorrow the chance of rain will be less than 80% is at least a half". For this logic we prove a decidability result. [ABSTRACT FROM AUTHOR]

Recently, we (Synthese, 199(5–6):13247–13281, 2021) proposed Kripke-like semantics for two quantum logics of interderminacy. These logics expand the vocabulary of standard Birkhoff-von Neumann propositional quantum logic with a pair of modal operators interpreted as “it is (in)determinate that”, allowing them to express in the object language statements such as “it is indeterminate that system S is spin-up in the x-direction”, as well as statements of any logical complexity involving ascriptions of (in)determinacy. We present an axiomatization of a logic closely related to one of these quantum logics of indeterminacy and prove that this axiomatization is sound and complete with respect to the Kripke-like semantics. We then prove that this logic is decidable. [ABSTRACT FROM AUTHOR]

The notion of a critical successor [5] in relational semantics has been central to most classic modal completeness proofs in interpretability logics. In this paper we shall work with a more general notion, that of an assuring successor. This will enable more concisely formulated completeness proofs, both with respect to ordinary and generalised Veltman semantics. Due to their interesting theoretical properties, we will devote some space to the study of a particular kind of assuring labels, the so‐called full labels and maximal labels. After a general treatment of assuringness, we shall apply it to obtain a completeness result for the modal logic ILP$\mathsf {ILP}$ w.r.t. generalised semantics for a restricted class of frames. [ABSTRACT FROM AUTHOR]

Although modal logic has significantly developed since the possible worlds semantics invention, today, it is recognized that a modal logic that uses only one type of modality is very restricted. In this article, I aim to provide the semantics and tableaux systems for some alethic-epistemic-doxastic logics. The basic system (T/T/KD*) is used to discuss the validity of some principles and some of Spinoza’s ideas on modal thinking, for he believed that the possibility and contingency ideas are defects of our cognition. Next, the system’s extensions based on are used to discuss the validity of the doxastic, epistemic, and alethic closure principles by means of the distinction between absolute and relative knowledge. Finally, the system is extended to develop a pair of conditional epistemic-doxastic logics to evaluate some skeptical statements. [ABSTRACT FROM AUTHOR]

We present a finitary version of Moss’ coalgebraic logic for T-coalgebras, where T is a locally monotone endofunctor of the category of posets and monotone maps. The logic uses a single cover modality whose arity is given by the least finitary subfunctor of the dual of the coalgebra functor T ∂ , and the semantics of the modality is given by relation lifting. For the semantics to work, T is required to preserve exact squares. For the finitary setting to work, Tω, and the semantics of the modality is given by relation lifting. For the semantics to work, T is required to preserve exact squares. For the finitary setting to work, T∂X. This in particular allows us to talk about the finite poset of subformulas for a given formula. The notion of a base is introduced generally for a category equipped with a suitable factorisation system. We prove that the resulting logic has the Hennessy-Milner property for the notion of similarity based on the notion of relation lifting. We define a sequent proof system for the logic, and prove its completeness. [ABSTRACT FROM AUTHOR] ω is required to preserve finite intersections. We develop a notion of a base for subobjects of TωX. This in particular allows us to talk about the finite poset of subformulas for a given formula. The notion of a base is introduced generally for a category equipped with a suitable factorisation system. We prove that the resulting logic has the Hennessy-Milner property for the notion of similarity based on the notion of relation lifting. We define a sequent proof system for the logic, and prove its completeness. [ABSTRACT FROM AUTHOR]

The logic BN4 was defined by R.T. Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of (relevant) implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims to define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete w.r.t. their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes. [ABSTRACT FROM AUTHOR]

In this paper, I will defend a new compositional semantics for single-domain free logic. This semantics makes use of a distinction between the semantic value of a singular term and its semantic referent. The semantic value of a singular term is conceived of as a set that either contains the semantic referent or no element at all. The semantic referent is the object that the term designates. Before I will introduce this new semantics for single-domain predicate and an S5-type modal logic in detail, I will present five related problems of compositionality of the standard semantics for these logical systems. After that I will show in detail how my new proposed alternative semantics can be used to solve nearly all of the outlined five problems. [ABSTRACT FROM AUTHOR]

Two-dimensional semantics, which can represent the distinction between a priority and (one kind of) necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger († ) operator of Stalnaker's "Assertion" (1978) in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed to Bayesian and Gricean contexts. Finally, I sketch the prospects for extending this two-dimensional upgrade to other kinds of modal logics for natural language. [ABSTRACT FROM AUTHOR]

Based on the Kripke structure, linear temporal logic and generalized possibility measure, this article studies the model checking problems of generalized possibilistic fuzzy linear temporal logic (GPoFTL). The generalized possibilistic Kripke structure is introduced to describe the system model. The syntax of GPoFTL, which includes fuzzy temporal operators such as ''soon'', ''presently'', ''gradually'', ''within'', ''last'', ''nearly always'', ''almost alwayss'', ''in the long distant future'', ''in the middle of'', ''nearly until'' and ''almost until'', and its language semantics and path semantics under generalized possibility measure are given. Next, we explain the semantics of fuzzy temporal operators through some examples and prove that GPoFTL is an extension of generalized possibilistic linear temporal logic in fuzzy time temporal logic. Furthermore, the GPoFTL model checking algorithm is given by explicit calculation formulas one by one for any GPoFTL formula involving fuzzy temporal operators using fuzzy matrix operations. Last, the algorithm of necessary threshold model checking of GPoFTL is studied using automata theory and its time complexity is discussed. [ABSTRACT FROM AUTHOR]

This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite. [ABSTRACT FROM AUTHOR]

Refinement relations, such as trace containment, simulation preorder, and their alternating versions, have been successfully applied in formal verification of concurrent systems. Recently, trace containment and simulation preorder have been adopted and developed in fuzzy systems, but the generalization of their alternating versions to fuzzy systems has not been investigated. To satisfy the need for modeling and analyzing fuzzy systems, this article proposes two types of refinement relations called fuzzy alternating trace containment and fuzzy alternating simulation preorder, based on fuzzy concurrent game structures (FCGSs) under the Gödel semantics. These two fuzzy notions inherit properties from the corresponding classical setting. For example, fuzzy alternating simulation preorder for finite-state FCGSs can be computed in polynomial time; fuzzy alternating simulation preorder is a fuzzy subset of fuzzy alternating trace containment, and both relations can be logically characterized in terms of fuzzy version of alternating-time temporal logic. These properties make the theory developed here suitable for the modeling and verification of fuzzy systems. [ABSTRACT FROM AUTHOR]

We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mathcal {M}$ , or an axiomatization S thereof, we find a modal logic M such that a modal sentence $\varphi $ is a theorem of M if and only if the sentence $\varphi ^*$ obtained by translating the modal operator with the truth predicate is true in $\mathcal {M}$ or a theorem of S under all such translations. To this end, we introduce a novel version of possible worlds semantics featuring both classical and nonclassical worlds and establish the completeness of a family of noncongruent modal logics whose internal logic is nonclassical with respect to this semantics. [ABSTRACT FROM AUTHOR]

The present paper develops a unified correspondence treatment of the Sahlqvist theory for possibility semantics, extending the results in the work by Yamamoto (2016, Journal of Logic and Computation , 27 , 2411–2430) from Sahlqvist formulas to the strictly larger class of inductive formulas and from the full possibility frames to filter-descriptive possibility frames. Specifically, we define the possibility semantics version of the algorithm Ackermann lemma based algorithm (ALBA) and an adapted interpretation of the expanded modal language used in the algorithm. One notable feature of the adaptation of ALBA to possibility frames setting is that the so-called nominal variables, which are interpreted as complete join-irreducibles in the standard setting, are interpreted as regular open closures of 'singletons' in the present setting, which is a novelty of the present paper. We prove the soundness of the algorithm with respect to both (the dual algebras of) full possibility frames and (the dual algebras of) filter-descriptive possibility frames, use the algorithm to give an alternative proof to the one in the work by Holliday (2016, Possibility frames and forcing for modal logic. UC Berkeley Working Paper in Logic and the Methodology of Science. URL. http://escholarship.org/uc/item/9v11r0dq) that the inductive formulas are constructively canonical and show that the algorithm succeeds on inductive formulas. We make some comparisons among different semantic settings in the design of the algorithms and fit possibility semantics into this broader picture. [ABSTRACT FROM AUTHOR]

The logic of change L C formulated by K. Świętorzecka, has its motivation coming from the Aristotelian theory of substantial change which is undrstood as a transformation consisting in the disappearing and becoming of individual substances. The transition: becoming/disapearing (and conversely) is expressed in L C by the primitive operator C, to be read: it changes that ..., and it is mapped by the progressively expanding L C language. We are interested in attributive changes of individual substances. We consider a formalism with two non-normal and not mutually definable operators of possible and necessary change, inspired by Aristotelian distinction of accidental and essential attributes. From L C we adopt the idea that temporal concepts are defined via change operators, and the idea of an expanding language. In what follows, We axiomatise our new logic L M C and describe its semantics, giving the proof of its completeness. We compare our formalism with selected modal logics. [ABSTRACT FROM AUTHOR]

This paper surveys a new perspective on tree automata and Monadic second-order logic (MSO) on infinite trees. We show that the operations on tree automata used in the translations of MSO-formulae to automata underlying Rabin's Tree Theorem (the decidability of MSO) correspond to the connectives of Intuitionistic Multiplicative Exponential Linear Logic (IMELL). Namely, we equip a variant of usual alternating tree automata (that we call uniform tree automata) with a fibered monoidal-closed structure which in particular handles a linear complementation of alternating automata. Moreover, this monoidal structure is actually Cartesian on non-deterministic automata, and an adaptation of a usual construction for the simulation of alternating automata by non-deterministic ones satisfies the deduction rules of the !(–) exponential modality of IMELL. (But this operation is unfortunately not a functor because it does not preserve composition.) Our model of IMLL consists in categories of games which are based on usual categories of two-player linear sequential games called simple games , and which generalize usual acceptance games of tree automata. This model provides a realizability semantics, along the lines of Curry–Howard proofs-as-programs correspondence, of a linear constructive deduction system for tree automata. This realizability semantics, which can be summarized with the slogan "automata as objects, strategies as morphisms," satisfies an expected property of witness extraction from proofs of existential statements. Moreover, it makes it possible to combine realizers produced as interpretations of proofs with strategies witnessing (non-)emptiness of tree automata. [ABSTRACT FROM AUTHOR]

It is shown here that the modal logic K and any extension of it with a finite number of axioms can be characterised by a polynomial semantics. Moreover, some comments are made about the possibility of using algebraic computation to determine deducibility on these logics. [ABSTRACT FROM AUTHOR]

We introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game's chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for the logics of lattices with weak negation and modal operators (Modal Lattice Logic). [ABSTRACT FROM AUTHOR]

Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. We identify complexity bounds for both problems, covering both lax and strict team semantics. By doing so, we come close to finalizing the programme that aims to completely classify the complexities of the basic reasoning problems for modal and propositional dependence, independence and inclusion logics. [ABSTRACT FROM AUTHOR]

Abstract The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Given their generally bad computational behavior of interval temporal logics, several techniques exist to produce decidable and computationally affordable temporal logics based on intervals. In this paper we take inspiration from Golumbic and Shamir's coarser interval algebras, which generalize the classical Allen's Interval Algebra, in order to define two previously unknown variants of Halpern and Shoham's logic (HS) based on coarser relations. We prove that, perhaps surprisingly, the satisfiability problem for the coarsest of the two variants, namely HS 3 , not only is decidable, but PSpace -complete in the finite/discrete case, and PSpace -hard in any other case; besides proving its complexity bounds, we implement a tableau-based satisfiability checker for it and test it against a systematically generated benchmark. Our results are strengthened by showing that not all coarser-than-Allen's relations are a guarantee of decidability, as we prove that the second variant, namely HS 7 , remains undecidable in all interesting cases. [ABSTRACT FROM AUTHOR]

We introduce the concept of a Zemanian logic above S4.3 and prove that an extension of S4.3 is the logic of a Tychonoff HED-space iff it is Zemanian. [ABSTRACT FROM AUTHOR]

This paper combines the ancient idea that causes necessitate their effects with Angelika Kratzer's semantics of modality. On the resulting view, causal claims quantify over restricted domains of possible worlds determined by two contextually determined parameters. I argue that this view can explain a number of otherwise puzzling features of the way we use and evaluate causal language, including the difference between causing an effect and being a cause of it, the sensitivity of causal judgements to normative facts, and the semantics of causal disagreements. [ABSTRACT FROM AUTHOR]

A semantics for quantified modal logic is presented that is based on Kleene’s notion of realizability. This semantics generalizes Flagg’s 1985 construction of a model of a modal version of Church’s Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church’s Thesis and a variant of a modal set theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra’s generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott’s graph model (for the untyped lambda calculus) which witnesses the failure of the stability of nonidentity. [ABSTRACT FROM PUBLISHER]

'The Craft of Formal Logic' is Arthur Prior's unpublished textbook, written in 1950-51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of 'entities' with modal character. Although he talks about these 'entities' only informally, and hesitates how to name them, using alternately the phrases 'possible states of affairs', 'chances', 'cases' or 'peculiar objects', he is nevertheless very clear that they should be the fundamental concept of any theory of modality as a form of quantity. Without the assumption that modal operators quantify over such modal objects, the modal system will be incapable of distinguishing an actually true proposition from a necessarily true one. Due to the fact that Prior never made any direct reference to this theory in his subsequently published papers, it remained largely unknown. The comparison of 'The Craft' with some of his papers on tense logic suggests that this early theory of modality underlies his later work on temporality. [ABSTRACT FROM AUTHOR]

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. [ABSTRACT FROM PUBLISHER]

In the topological semantics for propositional modal logic, S4 is known to be complete for the class of all topological spaces, for the rational line, for Cantor space, and for the real line. In the topological semantics for quantified modal logic, QS4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. The main result of the current paper is that QS4 is complete, indeed strongly complete, for the rational line. [ABSTRACT FROM PUBLISHER]

In this second and last paper of the two part investigation on “Modality and Axiomatic Theories of Truth” we apply a general strategy for constructing modal theories over axiomatic theories of truth to the theory Kripke-Feferman. This general strategy was developed in the first part of our investigation. Applying the strategy to Kripke-Feferman leads to the theory Modal Kripke-Feferman which we discuss from the three perspectives that we had already considered in the first paper, where we discussed the theory Modal Friedman-Sheard. That is, we first show that Modal Kripke-Feferman preserves theoremhood modulo translation with respect to modal operator logic. Second, we develop a modal semantics fitting the newly developed theory. Third, we investigate whether the modal predicate of Modal Kripke-Feferman can be understood along the lines of a proposal of Kripke, namely as a truth predicate modified by a modal operator. [ABSTRACT FROM PUBLISHER]

I examine Nathan Salmon's solution to the problem of trivialization, as it arises for conceptions of general term rigidity that construe it as identity of designation across possible worlds. I argue that he does not succeed in showing that some alleged general terms, such as "the colour of the sky" are non-rigid, but also that a small class of different examples that he presents, which can be construed as second order descriptions, are indeed non-rigid general terms, although for reasons different from those he thought. [ABSTRACT FROM AUTHOR]

This paper discusses an important puzzle about the semantics of indicative conditionals and deontic necessity modals ( should, ought, etc.): the Miner Puzzle (Parfit, ms; Kolodny and MacFarlane, J Philos 107:115-143, ). Rejecting modus ponens for the indicative conditional, as others have proposed, seems to solve a version of the puzzle, but is actually orthogonal to the puzzle itself. In fact, I prove that the puzzle arises for a variety of sophisticated analyses of the truth-conditions of indicative conditionals. A comprehensive solution requires rethinking the relationship between relevant information (what we know) and practical rankings of possibilities and actions (what to do). I argue that (i) relevant information determines whether considerations of value may be treated as reasons for actions that realize them and against actions that don't, (ii) incorporating this normative fact requires a revision of the standard ordering semantics for weak (but not for strong) deontic necessity modals, and (iii) an off-the-shelf semantics for weak deontic necessity modals, due to von Fintel and Iatridou, which distinguishes 'basic' and 'higher-order' ordering sources, and interprets weak deontic necessity modals relative to both, is well-suited to this task. The prominence of normative considerations in our proposal suggests a more general methodological lesson: formal semantic analysis of natural language modals expressing normative concepts demands that close attention be paid to the nature of the underlying normative phenomena. [ABSTRACT FROM AUTHOR]

The study begins with the outline of a general theory of truthmaking. Then, the author raises some issues for the theory in its application to modal languages and points to some specific answers. In the remaining part the paper explores some ramifications of this topic and discusses issues pertaining to meaning, truth and quantification in modal contexts and discourse. The upshot is to lay the ground for a theory of truthmakers for modal languages and modal truths. The author intends to investigate the prospects and ramifications of modal actualism, and against this background to develop a view which is anti-realist concerning the existence of possible worlds but which is free to use possible-worlds semantics. [ABSTRACT FROM AUTHOR]

Modal logics reason about properties of relational structures, and such properties are often characterized by axioms of modal logics. This connection between properties of relational structures and axioms of modal logics are called correspondence, and has been investigated well in the classical setting. The problem we consider is an intuitionistic version of this correspondence. In particular, this paper considers which part of the correspondence results known in classical setting is true for intuitionistic one. We first define the notion of robustness of axioms so that an axiom is robust if and only if its corresponding properties in classical and intuitionistic semantics are the same. Next we give a syntactically defined class of axioms, and prove that all axioms in this class are robust. This result is an analogue of the classical result by Sahlqvist, and its proof is partly based on a known proof of his theorem. [ABSTRACT FROM PUBLISHER]

The modern view of logical reasoning as modeled by a consequence operator (instead of simply by a set of theorems) has allowed for huge developments in the study of logic as an abstract discipline. Still, it is unable to explain why it is often the case that the same designation is used, in an ambiguous way, to describe several distinct modes of reasoning over the same logical language. A paradigmatic example of such a situation is ‘modal logic’, a terminology which can encompass reasoning over Kripke frames, but also over Kripke models, and in any case either locally (at a fixed world) or globally (at all worlds). Herein, we adopt a novel abstract notion of logic presented as a lattice-structured hierarchy of consequence operators, and explore some common proof-theoretic and model-theoretic ways of presenting such hierarchies through a collection of meaningful examples. In order to illustrate the usefulness of the notion of hierarchical consequence operators we address a few questions in the theory of combined logics, where a suitable abstract presentation of the logics being combined is absolutely essential. We show how to define the operation, in general, and we achieve a number of interesting preservation results for fibring within the context of 2-hierarchies. [ABSTRACT FROM PUBLISHER]

In the fourteenth century, Duns Scotus suggested that the proper analysis of modality required not just moments of time but also 'moments of nature'. In making this suggestion, he broke with an influential view first presented by Diodorus in the early Hellenistic period, and might even be said to have been the inventor of 'possible worlds'. In this essay we take Scotus' suggestion seriously devising first a double-index logic and then introducing the temporal order. Finally, using the temporal order, we define a modal order. This allows us to present modal logic without the usual interpretive questions arising concerning the relation called variously 'accessibility', 'alternativeness', and, 'relative possibility.' The system in which this analysis is done is one of those which have come to be called a hybrid logic. [ABSTRACT FROM AUTHOR]

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can, moreover, be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain-specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement and to maintain. This paper substantiates the authors’ firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility. [ABSTRACT FROM AUTHOR]

Fusion is a well-known form of combining normal modal logics endowed with a Hilbert calculi and a Kripke semantics. Herein, fusion is studied over logic systems using sequent calculi labelled with truth values and with a semantics based on a two-sorted algebra allowing, in particular, the representation of general Kripke structures. A wide variety of logics, including non-classical logics like, for instance, modal logics and intuitionistic logic can be presented by logic systems of this kind. A categorical approach of fusion is defined in the context of these logic systems. Preservation of soundness and completeness by fusion is studied. Soundness is preserved without further requirements, completeness is preserved under mild assumptions. [ABSTRACT FROM PUBLISHER]

We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4, and S5, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of "nested" or "tree-sequent" calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario. [ABSTRACT FROM AUTHOR]

We show that the bounded fragment of first–order logic and the hybrid language with 'downarrow' and 'at' operators are equally expressive even with polyadic modalities, but that their 'positive' fragments are equally expressive only for unary modalities. [ABSTRACT FROM AUTHOR]

Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules (however formulated) underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the standard readings, for example by adopting sequent rules with multiple conclusions. Another is to explore what readings the natural deduction rules do enforce. When the notion of a model of a rule is generalized, it is found that natural deduction rules express “intuitionistic” readings of their connectives. A third approach is presented here. The intuitionistic readings emerge when models of rules are defined globally, but the notion of a local model of a rule is also natural. Using this benchmark, natural deduction rules enforce exactly the classical readings of the connectives, while this is not true of axiomatic systems. This vindicates the historical motivation for natural deduction rules. One odd consequence of using the local model benchmark is that some systems of propositional logic are not complete for the semantics that their rules express. Parallels are drawn with incompleteness results in modal logic to help make sense of this. [ABSTRACT FROM AUTHOR]

Abstract: The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more primitive than linear logic. This revised point of view leads us to introduce tensor logic, a primitive variant of linear logic where negation is not involutive. After formulating its categorical semantics, we interpret tensor logic in a model based on Conway games equipped with a notion of payoff, in order to reflect the various resource policies of the logic: linear, affine, relevant or exponential. [Copyright &y& Elsevier]

van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic ( ETL: Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic ( DEL: Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged semantic framework, and its extension with the labeled past-operator “ Pϵ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc. [ABSTRACT FROM AUTHOR]

We look at two fundamental logical processes, often intertwined in planning and problem solving: inference and update. Inference is an internal process with which we uncover what is implicit in the information we already have. Update, on the other hand, is produced by external communication, usually in the form of announcements and in general in the form of observations, giving us information that might not have been available (even implicitly) before. Both processes have received attention from the logic community, usually separately. In this work, we develop a logical language that allows us to describe them together. We present syntax, semantics and a complete axiom system; we discuss similarities and differences with other approaches and mention how the work can be extended. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a class of semantic tableau systems for some counterfactual logics. All in all I will discuss 1024 systems. Possible world semantics is used to interpret our formal languages. Soundness results are obtained for every tableau system and completeness results for a large subclass of these. [ABSTRACT FROM AUTHOR]

We consider a family of noncongruential modal logics obtained by restricting the smallest classical modal logic E and some of its extensions. We show that these logics are also properly contained in Lemmon's S0.5; semantics for them are adapted from Cresswell's semantics for S0.5 and from neighborhood semantics for classical modal logics. Some extensions of these logics by means of usual modal logical axioms are also considered, and determination results proved. As a further example, we also show how to obtain restricted versions of some of Chellas and Segerberg's prenormal modal logics. [ABSTRACT FROM PUBLISHER]

Abstract: We develop possible worlds (Kripke) semantics at the categorical abstract model theoretic level provided by the so-called ‘institutions’. Our general abstract modal logic framework provides a method for systematic Kripke semantics extensions of logical systems from computing science and logic. We also extend the institution-independent method of ultraproducts of [R. Diaconescu, Institution-independent ultraproducts, Fundamenta Informaticæ 55 (3–4) (2003) 321–348] to possible worlds semantics and prove a fundamental preservation result for abstract modal satisfaction. As a consequence we develop a generic compactness result for possible worlds semantics. [Copyright &y& Elsevier]