A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers (...) an up-to-date and reliable guide essential for the student. (shrink)

We show that—unlike products of ‘transitive’ modal logics which are usually undecidable—their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite linear order or a finite transitive tree and the other is composed of structures like • transitive trees/partial orders/quasi-orders/linear orders or only finite such (...) structures expanding over time. The decidability proof is based on Kruskal’s tree theorem, and the proof of non-primitive recursiveness is by reduction of the reachability problem for lossy channel systems. The result is used to show that the dynamic topological logic interpreted in topological spaces with continuous functions is decidable if the number of function iterations is assumed to be finite. (shrink)

I expand modal normativism, a theory of metaphysical modality, to give a normativist account of metaphysical explanation. According to modal normativism, basic modal claims do not have a descriptive function, but instead have the normative function of enabling language users to express semantic rules that govern the use of ordinary non-modal vocabulary. However, a worry for modal normativism is that it doesn’t keep up with all of the important and interesting metaphysics we can do by giving and evaluating metaphysical explanations. (...) So, I advance modal normativism by arguing that metaphysical explanations also have a normative rather than descriptive function. In particular, non-causal explanatory claims have formal and semantic properties that make them expressively stricter than basic modal claims and so are better suited to express fine-grained aspects of semantic rules. A major payoff of my normativist account of metaphysical explanations is that it yields a plausible story about how we come to evaluate and know metaphysical explanations—we do this primarily by conceptual analysis. I also respond to a number of objections, including the objection that the epistemic payoffs of my view are not worth the metaphysical costs. (shrink)

This book on modal logic is especially designed for philosophy students. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dicto distinction. Discussion of philosophical (...) issues concerning the development of modal logic is woven into the text. The book uses natural deduction systems, which are widely regarded as the easiest to teach and use. It also includes a diagram technique that extends the method of truth trees to modal logic. This provides a foundation for a novel method for showing completeness that is easy to extend to quantifiers. This second edition contains a new chapter on logics of conditionals, an updated and expanded bibliography, and is updated throughout. (shrink)

Modal logic provides an elegant way to understand the notion of potential infinity. This raises the question of what the right modal logic is for reasoning about potential infinity. In this article I identify a choice point in determining the right modal logic: Can a potentially infinite collection ever be expanded in two mutually incompatible ways? If not, then the possible expansions are convergent; if so, then the possible expansions are branching. When possible expansions are convergent, the right modal logic (...) is S4.2, and a mirroring theorem due to Linnebo allows for a natural potentialist interpretation of mathematical discourse. When the possible expansions are branching, the right modal logic is S4. However, the usual box and diamond do not suffice to express everything the potentialist wants to express. I argue that the potentialist also needs an operator expressing that something will eventually happen in every possible expansion. I prove that the result of adding this operator to S4 makes the set of validities Pi-1-1 hard. This result makes it unlikely that there is any natural translation of ordinary mathematical discourse into the potentialist framework in the context of branching possibilities. (shrink)

Modal logic provides an elegant way to understand the notion of potential infinity. This raises the question of what the right modal logic is for reasoning about potential infinity. In this article I identify a choice point in determining the right modal logic: Can a potentially infinite collection ever be expanded in two mutually incompatible ways? If not, then the possible expansions are convergent; if so, then the possible expansions are branching. When possible expansions are convergent, the right modal logic (...) is S4.2, and a mirroring theorem due to Linnebo allows for a natural potentialist interpretation of mathematical discourse. When the possible expansions are branching, the right modal logic is S4. However, the usual box and diamond do not suffice to express everything the potentialist wants to express. I argue that the potentialist also needs an operator expressing that something will eventually happen in every possible expansion. I prove that the result of adding this operator to S4 makes the set of validities Pi-1-1 hard. This result makes it unlikely that there is any natural translation of ordinary mathematical discourse into the potentialist framework in the context of branching possibilities. (shrink)

This booklet is a Korean adaptation and translation of Part VIII of forall x: Calgary (Fall 2021 edition), which is intended to be introductory material for modal logic. The original text is based on Robert Trueman's A Modal Logic Primer, which is revised and expanded by Richard Zach and Aaron Thomas-Bolduc in forall x: Calgary. (forall x: Calgary is based on forall x: Cambridge by Tim Button, which is in turn based on forall x by P. D. Magnus, and also (...) includes material from forall x: Lorain County Remix by Cathal Woods and J. Robert Loftis.) This booklet is licensed under a Creative Commons Attribution 4.0 license. (shrink)

We present the propositional logic LEC for the two epistemic modalities of current and stable knowledge used by an agent who system-atically enriches his language. A change in the linguistic resources of an agent as a result of certain cognitive processes is something that commonly happens. Our system is based on the logic LC intended to formalize the idea that the occurrence of changes induces the passage of time. Here, the primitive operator C read as: it changes that, defines (...) the temporal succession of states of the world. The notion of current knowledge concerns variable components of the world and it may change over time. We represent it by the primitive operator k read as: the agent currently knows that, and assume that it has S5 properties. The second type of knowledge, symbolized by the primitive operator K read as: the agent stably knows that, relates to constant components of the world and it does not change. As a result of the axiomatic entanglement of C, K and k we show that stable knowledge satisfies axioms of S4.3. K and k modalities are not mutually definable, stable knowledge implies the current one and if the latter never changes, then it comes to be stable. The combination of K and k with the idea of an expanding language allows questioning of the so-called perfect recall principle. It cannot be maintained for both types of knowledge just because of changes in the vocabulary of the agent and possibly the growing spectrum of possible states of the world. We interpret LEC in the semantics of histories of epistemic changes and show that it is complete. Finally, we compare our logic with selected epistemic logics based on the concept of linear discrete time. (shrink)

Given a class \ of models, a binary relation \ between models, and a model-theoretic language L, we consider the modal logic and the modal algebra of the theory of \ in L where the modal operator is interpreted via \. We discuss how modal theories of \ and \ depend on the model-theoretic language, their Kripke completeness, and expressibility of the modality inside L. We calculate such theories for the submodel and the quotient relations. We prove a downward Löwenheim–Skolem (...) theorem for first-order language expanded with the modal operator for the extension relation between models. (shrink)

This is the second edition of an award-winning 1981 book (Princeton University Press and Basil Blackwell, based on the author’s doctoral dissertation) considered to be a classic in the philosophy of language movement known variously as the New Theory of Reference or the Direct-Reference Theory, as well as in the metaphysics of modal essentialism that is related to this philosophy of language.

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

Recently, researchers have expanded the investigation into attentional biases toward positive stimuli; however, few studies have examined attentional biases toward positive auditory information. In three experiments, the present study employed an emotional spatial cueing task using emotional sounds as cues and auditory stimuli or visual stimuli as targets to explore whether auditory or visual spatial attention could be modulated by positive auditory cues. Experiment 3 also examined the temporal dynamics of cross-modal auditory bias toward positive natural sounds using event-related potentials. (...) The behavioral results of the three experiments consistently demonstrated that response times to targets were faster after positive auditory cues than they were after neutral auditory cues in the valid condition, indicating that healthy participants showed a selective auditory attentional bias and cross-modal attentional bias toward positive natural sounds. The results of Experiment 3 showed that N1 amplitudes were more negative after positive sounds than they were after neutral sounds, which further provided electrophysiological evidence that positive auditory information enhances attention at early stages in healthy adults. The results of the experiments performed in the present study suggest that humans exhibit an attentional bias toward positive natural sounds. (shrink)

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

This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking (...) coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators. (shrink)

In a recent paper in this journal Duncan Pritchard responds to an objection to the modal account of risk pressed by Ebert, Smith and Durbach ( 2020 ). In this paper, I expand upon the objection and argue that it still stands. I go on to consider a more general question raised by this exchange – whether risk is ‘objective’, or whether it is something that varies from one perspective to another.

This essay expands upon the suggestion that Lessing's infamous ‘ditch’ is actually three ditches: temporal, metaphysical, and existential gaps. It examines the complex problems these ditches raise, and then proposes that Kierkegaard's Fragments and Postscript exhibit a similar triadic organizational structure, which may signal a deliberate attempt to engage and respond to Lessing's three gaps. Viewing the Climacean project in this way offers an enhanced understanding of the intricacies of Lessing's rationalist approach to both religion and historical truth, and illuminates (...) Climacus's subjective response to Lessing. (shrink)

The logic of change 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 by the primitive operator C, to be read: it changes that …, and it is mapped by the progressively expanding 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 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 and describe its semantics, giving the proof of its completeness. We compare our formalism with selected modal logics. (shrink)

We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic and formal (...) logics, respectively. We also show that, for most “natural” first-order modal logics, the two-variable fragment with a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable, regardless of whether we consider semantics with expanding or constant domains. These include all sublogics of QKTB, QGL, and QGrz—among them, QK, QT, QKB, QD, QK4, and QS4. (shrink)

This paper investigates a first-order extension of GL called \. We outline briefly the history that led to \, its key properties and some of its toolbox: the \emph{conservation theorem}, its cut-free Gentzenisation, the ``formulators'' tool. Its semantic completeness is fully stated in the current paper and the proof is retold here. Applying the Solovay technique to those models the present paper establishes its main result, namely, that \ is arithmetically complete. As expanded below, \ is a first-order modal logic (...) that along with its built-in ability to simulate general classical first-order provability―"\" simulating the the informal classical "\"―is also arithmetically complete in the Solovay sense. (shrink)

The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the (...) same expressive power on the level of frames with the language \ under the relational semantics for classical modal logic. (shrink)

ABSTRACT George Gargov was an active pioneer in the ‘Sofia School’ of modal logicians. Starting in the 1970s, he and his colleagues expanded the scope of the subject by introducing new modal expressive power, of various innovative kinds. The aim of this paper is to show some general patterns behind such extensions, and review some very general results that we know by now, 20 years later. We concentrate on simulation invariance, decidability, and correspondence. What seems clear is that ‘modal logic’ (...) as a genre of logical systems has a much wider scope than originally conceived, and that we have not reached its limits yet. (shrink)

The dissertation introduces new sequent-calculi for free first- and second-order logic, and a hyper-sequent calculus for modal logics K, D, T, B, S4, and S5; to attain the calculi for the stronger modal logics, only external structural rules need to be added to the calculus for K, while operational and internal structural rules remain the same. Completeness and cut-elimination are proved for all calculi presented.Philosophically, the dissertation develops an inferentialist, or proof-theoretic, theory of meaning. It takes as a starting point (...) that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. The dissertation develops a theory of quantification as marking coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators.Abstract prepared by Andrew ParisiE-mail: [email protected]: https://opencommons.uconn.edu/dissertations/1480/. (shrink)

ABSTRACT George Gargov was an active pioneer in the ‘Sofia School’ of modal logicians. Starting in the 1970s, he and his colleagues expanded the scope of the subject by introducing new modal expressive power, of various innovative kinds. The aim of this paper is to show some general patterns behind such extensions, and review some very general results that we know by now, 20 years later. We concentrate on simulation invariance, decidability, and correspondence. What seems clear is that ‘modal logic’ (...) as a genre of logical systems has a much wider scope than originally conceived, and that we have not reached its limits yet. (shrink)

Günter Wagner’s Homology, Genes, and Evolutionary Innovation collects and synthesizes a vast array of empirical data, theoretical models, and conceptual analysis to set out a progressive research program with a central theoretical commitment: the genetic theory of homology. This research program diverges from standard approaches in evolutionary biology, provides sharpened contours to explanations of the origin of novelty, and expands the conceptual repertoire of evolutionary developmental biology. I concentrate on four aspects of the book in this essay review: the genetic (...) theory of homology and character identity networks; the implications for how we explain evolutionary novelties; the expanded set of concepts surrounding homology, and the epistemological conflicts between Wagner’s viewpoint and functionally-oriented evolutionary biology, as well as differences with other Evo–devo researchers. Together these have ramifications for how we interpret different explanatory approaches to evolutionary phenomena and understand relationships between the usefulness of concepts and the reality they represent. (shrink)

This paper expands upon the work by Wang (Proceedings of TARK, pp. 493–512, 2017) who proposes a new framework based on quantifier-free predicate language extended by a new bundled modality \(\exists x\Box \) and axiomatizes the logic over S5 frames. This paper first gives complete axiomatizations of the logics over K, D, T, 4, S4 frames with increasing domains and constant domains, respectively. The systems w.r.t. constant domains feature infinitely many additional rules defined inductively than systems w.r.t. increasing domains. In (...) the second part of the paper, we show that these rules are admissible in the systems without them by providing a general strategy for proving completeness theorems for the logics without these rules over constant domain models (also increasing domain models). (shrink)

The goal of this paper is an interpretation of Aristotle's modal syllogistics closely oriented on the text using the resources of modern modal predicate logic. Modern predicate logic was successfully able to interpret Aristotle's assertoric syllogistics uniformly , that is, with one formula for universal premises. A corresponding uniform interpretation of modal syllogistics by means of modal predicate logic is not possible. This thesis does not imply that a uniform view is abandoned. However, it replaces the simple unity of the (...) assertoric by the complex unity of the modal. The complexity results from the fact that though one formula for universal premises is used as the basis, it must be moderated if the text requires . Aristotle introduces his modal syllogistics by expanding his assertoric syllogistics with an axiom that links two apodictic premises to yield a single apodictic sentence . He thus defines a regular modern modal logic. By means of the regular modal logic that is thus defined, he is able to reduce the purely apodictic syllogistics to assertoric syllogistics. However, he goes beyond this simple structure when he looks at complicated inferences. In order to be able to link not only premises of the same modality, but also premises with different modalities, he introduces a second axiom, the T-axiom, which infers from necessity to reality or - equivalently - from reality to possibility. Together, the two axioms, the axiom of regularity and the T-axiom, define a regular T-logic. It plays an important role in modern logic. In order to be able to account for modal syllogistics adequately as a whole, another modern axiom is also required, the so-called B-axiom. It is very difficult to decide whether Aristotle had the B-axiom. The two last named axioms are sufficient to achieve the required contextual moderation of the basic formula for universal propositions. (shrink)

We propose a generalization of Sahlqvist formulas to polyadic modal languages by representing such languages in a combinatorial PDL style and thus, in particular, developing what we believe to be the right syntactic approach to Sahlqvist formulas at all. The class of polyadic Sahlqvist formulas PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

To reason about continuous processes in some areas of artificial intelligence and embedded systems one has to express real-time properties. For such purpose a real-time logic has to be considered. Various such logics have been proposed. Some of these formalisms interpret formulas over intervals of time. These are called interval logics. Zhou Chaochen and Michael Hansen have introduced one such first-order interval logic called Neighborhood Logic (NL) which has two expanding modalities ◊r and ◊l. They have shown the (...) adequacy of these modalities by deriving other unary and binary modalities from them; in particular, they show that chop can be expressed in terms of these modalities. The logic is subsequently expanded to get a Duration Calculus (called DC/nl) by expressing temporal variables as integrals of state variables. Liveness and fairness properties of a computing system can now be expressed in DC/nl by means of neighborhood (expanding) modalities. We take up an investigation of DC/nl in detail. We present a proof system for it. We further show that most of the results that hold in the original Duration Calculus continue to hold in our logic with some modifications. In this process we discuss soundness, completeness, and decidability results for DC/nl. Thus this paper establishes DC/nl as a useful formalism for specifying and verifying properties of real-time computing systems. (shrink)

The distinction between true belief and knowledge is one of the most fundamental in philosophy, and a remarkable effort has been dedicated to formulating the conditions on which true belief constitutes knowledge. For decades, much of this epistemological undertaking has been dominated by a single strategy, referred to here as the modal approach. Shared by many of the most widely influential constraints on knowledge, including the sensitivity, safety, and anti-luck/risk conditions, this approach rests on a key underlying assumption — the (...) modal profiles available to known and unknown beliefs are in some way asymmetrical. The first aim of this paper is to deconstruct this assumption, identifying its plausibility with the way in which epistemologists frequently conceptualize human perceptual systems as excluding certain varieties of close error under conditions conducive to knowledge acquisition. The second aim of this paper is to then argue that a neural phase phenomenon indicates that this conceptualization is quite likely mistaken. This argument builds on the previous introduction of this neural phase to the context of epistemology, expanding the use of neural phase cases beyond relatively narrow questions about epistemic luck to a much more expansive critique of the modal approach as a whole. (shrink)

Many philosophers believe that there is a causal condition on perception, and that this condition is a conceptual truth about perception. A highly influential argument for this claim is based on intuitive responses to Gricean-style thought experiments. Do the folk share the intuitions of philosophers? Roberts et al. (2016) presented participants with two kinds of cases: Blocker cases (similar to Grice’s case involving a mirror and a pillar) and Non-Blocker cases (similar to Grice’s case involving a clock and brain stimulation). (...) They found that a substantial minority agreed that seeing occurs in the Non-Blocker cases, and that in the Blocker cases significantly less agreed that seeing occurs. They thus hypothesized that folk intuitions better align with a no blocker condition than with a causal condition. This paper continues this line of enquiry with two new experiments. The paper investigates the generality and robustness of Roberts et al.’s findings by expanding the sense modalities tested from only vision to audition and olfaction as well. The paper also uses Gricean-style thought experiments as a case study for investigating the “reflection defense” against the negative project in experimental philosophy. Our results replicate and extend Roberts et al.’s study and support their hypothesis that folk intuitions better align with a no blocker condition. They also provide an empirical reason to doubt the reflection defense. (shrink)

Morten Frederiksen explores Carl Gustav Jung's elusive notion of synchronicity from a transrational perspective and relates synchronicity to the transpersonality of the "All-One". This is done by expanding the content and meaning of Wolfgang Dietrich's layers of Elicitive Conflict Mapping (ECM) through re-relating them to Ken Wilber's model of the structures of consciousness; with synchronicity as the literal connecting principle. The result, then, is an expanded notion of the transrational peace philosophy which includes Wilber's model of stages shorn of (...) its evolutionary slant and fathoms synchronicity in its theoretical outlook and practical application. Contents A Transrational Approach to Peace Studies through processing the Topic of Synchronicity Jungian Psychology and his Concept of Synchronicity Transrational Peace Philosophy and Consciousness Development Seven different Structures of Consciousness Consequences of Synchronicity for a transrational-oriented Peace Philosophy and Practice Target Groups Lecturers and Students of Psychology, Peace Students and Conflict Transformation Researchers Practitioners in the Field of Elicitive Conflict Transformation About the Author Morten Frederiksen is a Peace Researcher from the MA Program in Peace, Security, Development and International Conflict Transformation at the University of Innsbruck, Austria, and Coordinator of the Danish Development Aid Agency "U-landsforeningen Svalerne". (shrink)

Let α be an arbitrary infinite ordinal, and. In [26] we studied—using algebraic logic—interpolation and amalgamation for an extension of first order logic, call it, with α many variables, using a modal operator of a unimodal logic that contributes to the semantics. Our algebraic apparatus was the class of modal cylindric algebras. Modal cylindric algebras, briefly, are cylindric algebras of dimension α, expanded with unary modalities inheriting their semantics from a unimodal logic such as, or. When modal cylindric algebras (...) based on are just cylindric algebras, that is to say,. This paper is a sequel to [26], where we study algebraically other properties of. We study completeness and omitting types (s) for s by proving several representability results for so‐called dimension complemented and locally finite. Furthermore, we study the notion of atom‐canonicity for, the variety of n‐dimensional modal cylindric algebras. Atom canonicity, a well known persistence property in modal logic, is studied in connection to for, which is restricted to the first n variables. We further continue our study of interpolation in [26] for algebraizable extensions of by studying using both algebraic logic and category theory. Our main results on are Theorems 3.7, 4.4 & 4.6, while our main results on amalgamation are Theorems 5.7, 5.10, 5.13 & 5.16. (shrink)

Many philosophers believe that there is a causal condition on perception, and that this condition is a conceptual truth about perception. A highly influential argument for this claim is based on intuitive responses to Gricean style thought experiments. Do the folk share the intuitions of philosophers? Roberts et al. (2016) presented participants with two kinds of cases: Blocker cases (similar to Grice’s case involving a mirror and a pillar) and Non-Blocker cases (similar to Grice’s case involving a clock and brain (...) stimulation). They found that a substantial minority agreed that seeing occurs in the Non-Blocker cases, and that in the Blocker cases significantly less agreed that seeing occurs. They thus hypothesized that folk intuitions better align with a no blocker condition than with a causal condition. This paper continues this line of enquiry with two new experiments. The paper investigates the generality and robustness of Roberts et al.’s findings by expanding the sense modalities tested from only vision to audition and olfaction as well. The paper also uses Gricean style thought experiments as a case study for investigating the “reflection defense” against the negative project in experimental philosophy. Our results replicate and extend Roberts et al.’s study and support their hypothesis that folk intuitions better align with a no blocker condition. They also provide an empirical reason to doubt the reflection defense. (shrink)

Quantified hybrid logic is quantified modal logic extended with apparatus for naming states and asserting that a formula is true at a named state. While interpolation and Beth's definability theorem fail in a number of well-known quantified modal logics , their counterparts in quantified hybrid logic have these properties. These are special cases of the main result of the paper: the quantified hybrid logic of any class of frames definable in the bounded fragment of first-order logic has the interpolation property, (...) irrespective of whether varying, constant, expanding, or contracting domains are assumed. (shrink)

The aim of the present study is to evaluate Sonja Foss’s Rhetorical Schema for the Evaluation of Visual Imagery as well as reflect upon several points for further consideration; and finally suggest a renewed triadic approach as a method for analyzing art-relevant visual imagery. The triadic approach to be discussed assumes three correlative layers: the intellectual knowledge, function of the artistic content as the visual representational component, and aesthetics as modality. This study will include the analysis of a print advertisement (...) that used an artwork as its content of visual rhetoric, and this will inform further discussions on the proposed approach. The contribution of this renewed triadic approached to the field of visual rhetoric has the advantage of expanding and possibly improving rhetorical analysis methods of visual imagery. (shrink)

Past public announcement operators have been defined in Hoshi and Yap :259–281, 2009) and Yap, to describe an agent’s knowledge before an announcement occurs. These operators rely on branching-time structures that do not mirror the traditional, relativization-based semantics of public announcement logic, and favor a historical reading of past announcements. In this paper, we introduce reverse public announcement operators that are interpreted on expanded models. Our model expansion adds accessibility links from an epistemic model \ to a filtrated submodel of (...) the canonical model for \. Here \ is the minimal normal modal logic together with \ axioms for the universal operator U. This yields a highly general pre-announcement version of \ that makes our operators potentially useful for studying non-standard interpretations of rescinded announcements in PAL. Indeed, we find that our reverse announcement operators cannot be represented by product update, and that they have an intimate connection with the knowledge forgetting of Zhang and Zhou :1525–1537, 2009). We show that the logic resulting from adding reverse announcements to PAL is sound and complete. (shrink)

We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the two-variable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of practically all standard modal logics like K, K4, GL, S4, S5, K4.1, S4.2, GL.3, etc.). For many quantified modal logics, including (...) those in the standard nomenclature above, even the monadic two-variable fragments turn out to be undecidable. (shrink)

One of the classical arguments for the existence of God is the ontological argument. In the second half of the twentieth century, this argument was updated, and triggered new philosophical discussions under the title of “modal ontological argument.” These discussions have expanded with the emergence of the modal versions of the cosmological argument. However, despite the intense interest in arguments for the existence of God, the contemporary scholarship in the philosophy of religion largely overlooks the problem as to whether God (...) is unique or not. In this paper, I aim to update Taftazānī’s argument for the uniqueness of God by means of the conceptual tools of the possible world semantics. Taftazānī’s argument is known as burhān al-tamānu in the Islamic kalām, and aims to show that postulating two omnipotent gods will result in contradictions due to a possible conflict between the two divine wills. The term tamānu refers to the conflict between these wills. So, I argue that this argument, supplemented by the conclusion of the modal ontological or cosmological argument, shows that there is only one God. I call this extended argument “A Modal Argument for the Uniqueness of God.”. (shrink)

The paper expands upon the work by Wang [4], who proposes a new framework based on quantifier-free predicate language extended by a new modality ∃x□\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exists x\Box $$\end{document} and axiomatizes the logic over S5 frames. This paper gives the logics over K, D, T, 4, S4 frames with increasing and constant domains. And we provide a general strategy for proving completeness theorems for logics w.r.t. the increasing domain and logics w.r.t. the constant (...) domain respectively. (shrink)

The Royal Institute of Philosophy volume of which this paper is an introduction is on the theme of ‘Expanding Horizons’. But what does it mean for philosophy to fruitfully expand its horizons? The contributions to the volume suggest at least five profitable ways. First, by looking to other philosophical traditions for new perspectives on familiar questions and alternative methods, questions, and ways of understanding. Second, by looking to what has been neglected or overlooked in our own histories of thought. (...) Third, by developing novel methods, in addition to argument, for investigating philosophical issues. Fourth, by embracing different modalities for doing philology, such as the literary. Fifth, by reflecting on the practice of comparative philosophy to better understand the extent to which philosophy can and should be universal. Together, these approaches both increase the range of voices heard in philosophy and the scope and ambition of the discipline. (shrink)

We show a sentence and modal square of opposition and equivalence to be expanded into an hexagon according to oe suggestion from William of Sherwood. This expansión is permittedby two sentence and modal rules.The logical relations of the square allow us to formulate several theorems in order to show a glimpse of the Medieval Logic complexity.

On Peirce’ view, we can perceive many things commonly thought not to be perceptible—or thought to be ‘abstract’—including but not necessarily limited to (some) generals or universals, habits or law-like properties, modal properties, and semeiotic properties (sign relations). My contention turns on his arguments in ‘Some Consequences’ that ‘no cognition of ours is absolutely determinate’, his mature account of perception, particularly his criteria for what counts as perception and what does not, his analysis of the predication of concepts (i.e. his (...) pragmaticism), his claims in the 1903 Harvard lectures that we directly perceive Thirdness, and his realism about generals, habits, modalities, and sign relations. (shrink)

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example has been provided (...) to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation operators and the (...) pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)