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A New Introduction to Modal Logic

New York: Routledge. Edited by M. J. Cresswell (1996)

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  1. Aristotle's Modal Proofs: Prior Analytics A8-22 in Predicate Logic.Adriane Rini - 2010 - Dordrecht, Netherland: Springer.
    Aristotle’s modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a ‘realm of darkness’. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle’s results. This volume provides a simple interpretation of Aristotle’s modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as ‘horse’, ‘plant’ or ‘man’, which name things in virtue of features those things must have, and green terms, such as (...)
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  • Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
    This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...)
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  • Modality, Semantics and Interpretations: The Second Asian Workshop on Philosophical Logic.Shier Ju, Hu Liu & Hiroakira Ono (eds.) - 2015 - Heidelberg, Germany: Springer.
    This contributed volume includes both theoretical research on philosophical logic and its applications in artificial intelligence, mostly employing the concepts and techniques of modal logic. It collects selected papers presented at the Second Asia Workshop on Philosophical Logic, held in Guangzhou, China in 2014, as well as a number of invited papers by specialists in related fields. The contributions represent pioneering philosophical logic research in Asia.
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  • Natural Deduction, Hybrid Systems and Modal Logics.Andrzej Indrzejczak - 2010 - Dordrecht, Netherland: Springer.
    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.
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  • Non-Measurability, Imprecise Credences, and Imprecise Chances.Yoaav Isaacs, Alan Hájek & John Hawthorne - 2021 - Mind 131 (523):892-916.
    – We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...)
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  • Remarks on Logic and Critical Thinking.Mudasir Ahmad Tantray - 2021 - Bilaspur, Chhattisgarh 495001, India: Rudra Publications.
    This work is compiled for the students, research scholars, academicians, who are interested in logic, philosophy, mathematics and critical thinking. The main objective of this book is to provide basics or fundamental knowledge for those who have chosen logic as their subject in order to develop analytical and critical ideas. It has been primarily developed to serve as an introductory piece of work which includes explanatory notes on different courses like Inductive logic, Deductive logic, propositional logic, Symbolic logic, Quantification logic, (...)
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  • Non-Boolean classical relevant logics II: Classicality through truth-constants.Tore Fjetland Øgaard - 2021 - Synthese (3-4):1-33.
    This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics (...)
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  • Anti-Realism and Modal-Epistemic Collapse: Reply to Marton.Jan Heylen - 2021 - Erkenntnis 88 (1):397-408.
    Marton ( 2019 ) argues that that it follows from the standard antirealist theory of truth, which states that truth and possible knowledge are equivalent, that knowing possibilities is equivalent to the possibility of knowing, whereas these notions should be distinct. Moreover, he argues that the usual strategies of dealing with the Church–Fitch paradox of knowability are either not able to deal with his modal-epistemic collapse result or they only do so at a high price. Against this, I argue that (...)
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  • Quantitative and Qualitative Approaches to Generalization and Replication–A Representationalist View.Matthias Borgstede & Marcel Scholz - 2021 - Frontiers in Psychology 12.
    In this paper, we provide a re-interpretation of qualitative and quantitative modeling from a representationalist perspective. In this view, both approaches attempt to construct abstract representations of empirical relational structures. Whereas quantitative research uses variable-based models that abstract from individual cases, qualitative research favors case-based models that abstract from individual characteristics. Variable-based models are usually stated in the form of quantified sentences. This syntactic structure implies that sentences about individual cases are derived using deductive reasoning. In contrast, case-based models are (...)
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  • Computer Simulations, Machine Learning and the Laplacean Demon: Opacity in the Case of High Energy Physics.Florian J. Boge & Paul Grünke - forthcoming - In Andreas Kaminski, Michael Resch & Petra Gehring (eds.), The Science and Art of Simulation II.
    In this paper, we pursue three general aims: (I) We will define a notion of fundamental opacity and ask whether it can be found in High Energy Physics (HEP), given the involvement of machine learning (ML) and computer simulations (CS) therein. (II) We identify two kinds of non-fundamental, contingent opacity associated with CS and ML in HEP respectively, and ask whether, and if so how, they may be overcome. (III) We address the question of whether any kind of opacity, contingent (...)
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  • New Modification of the Subformula Property for a Modal Logic.Mitio Takano - 2020 - Bulletin of the Section of Logic 49 (3):255-268.
    A modified subformula property for the modal logic KD with the additionalaxiom □ ◊ ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown. The finite model property as well as decidability for the logic follows from this.
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  • Mechanized analysis of Anselm’s modal ontological argument.John Rushby - 2020 - International Journal for Philosophy of Religion 89 (2):135-152.
    We use a mechanized verification system, PVS, to examine the argument from Anselm’s Proslogion Chapter III, the so-called “Modal Ontological Argument.” We consider several published formalizations for the argument and show they are all essentially similar. Furthermore, we show that the argument is trivial once the modal axioms are taken into account. This work is an illustration of Computational Philiosophy and, in addition, shows how these methods can help detect and rectify errors in modal reasoning.
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  • Para Todxs: Natal - uma introdução à lógica formal.P. D. Magnus, Tim Button, Robert Loftis, Robert Trueman, Aaron Thomas Bolduc, Richard Zach, Daniel Durante, Maria da Paz Nunes de Medeiros, Ricardo Gentil de Araújo Pereira, Tiago de Oliveira Magalhães, Hudson Benevides, Jordão Cardoso, Paulo Benício de Andrade Guimarães & Valdeniz da Silva Cruz Junior - 2022 - Natal-RN: PPGFIL-UFRN.
    Livro-texto de introdução à lógica, com (mais do que) pitadas de filosofia da lógica, produzido como uma versão revista e ampliada do livro Forallx: Calgary. Trata-se da versão de 13 de outubro de 2022. Comentários, críticas, correções e sugestões são muito bem-vindos.
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  • Counterpart theories for everyone.Achille C. Varzi - 2020 - Synthese 197 (11):4691-4715.
    David Lewis’s counterpart theory is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic, suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in which (...)
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  • Two morals about a modal paradox.Alexander Roberts - 2020 - Synthese 198 (10):9873-9896.
    Chisholm’s paradox serves as an important constraint on our modal theorising. For example, one lesson of the paradox is that widely accepted essentialist theses appear incompatible with metaphysical necessity obeying a logic that includes S4. However, this article cautions against treating Chisholm’s paradox in isolation, as a single line of reasoning. To this end, the article outlines two crucial morals about Chisholm’s paradox which situate the paradox within a broad family of paradoxes. Each moral places significant constraints on the paradox’s (...)
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  • Higher-Order Evidence.Kevin Dorst - 2024 - In Maria Lasonen-Aarnio & Clayton Littlejohn (eds.), The Routledge Handbook of the Philosophy of Evidence. New York, NY: Routledge. pp. 176-194.
    On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.
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  • Advances in Modal Logic, Vol. 13.Nicola Olivetti & Rineke Verbrugge (eds.) - 2020 - College Publications.
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  • The Many and the One: A Philosophical Study of Plural Logic.Salvatore Florio & Øystein Linnebo - 2021 - Oxford, England: Oxford University Press.
    Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between (...)
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  • Vagueness-Induced Counterexamples to Modus Tollens.Tom Beevers - 2021 - Proceedings of the Aristotelian Society 120 (3):405-416.
    I argue that vagueness produces counterexamples to modus tollens. I begin by outlining cases where indicative and counterfactual conditionals seem intuitively to be determinate even when their antecedents are borderline and their consequents are determinately false. Accepting these intuitions has some revisionary implications; however, rejecting them leads to unacceptable consequences for our knowledge of conditionals. I thus take it that we should accept that our intuitions are reliable. I show it follows that modus tollens fails. I conclude by defending this (...)
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  • The Moral Law and The Good in Temporal Modal Logic with Propositional Quantifiers.Daniel Rönnedal - 2020 - Australasian Journal of Logic 17 (1):22-69.
    The Moral Law is fulfilled iff everything that ought to be the case is the case, and The Good is realised in a possible world w at a time t iff w is deontically accessible from w at t. In this paper, I will introduce a set of temporal modal deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any (...)
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  • Rational requirements for suspended judgment.Luis Rosa - 2021 - Philosophical Studies 178 (2):385-406.
    How does rationality bind the agnostic, that is, the one who suspends judgment about whether a given proposition is true? In this paper I explore two alternative ways of establishing what the rational requirements of agnosticism are: the Lockean–Bayesian framework and the doxastic logic framework. Each of these proposals faces strong objections. Fortunately, however, there is a rich kernel of requirements of agnosticism that are vindicated by both of them. One can then endorse the requirements that belong to that kernel (...)
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  • Logic, Metalogic and Neutrality.Timothy Williamson - 2013 - Erkenntnis 79 (Suppl 2):211-231.
    The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were (...)
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  • Uniform Lyndon interpolation property in propositional modal logics.Taishi Kurahashi - 2020 - Archive for Mathematical Logic 59 (5-6):659-678.
    We introduce and investigate the notion of uniform Lyndon interpolation property which is a strengthening of both uniform interpolation property and Lyndon interpolation property. We prove several propositional modal logics including \, \, \ and \ enjoy ULIP. Our proofs are modifications of Visser’s proofs of uniform interpolation property using layered bisimulations Gödel’96, logical foundations of mathematics, computer science and physics—Kurt Gödel’s legacy, Springer, Berlin, 1996). Also we give a new upper bound on the complexity of uniform interpolants for \ (...)
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  • On Correspondence of Standard Modalities and Negative Ones on the Basis of Regular and Quasi-regular Logics.Krystyna Mruczek-Nasieniewska & Marek Nasieniewski - 2020 - Studia Logica 108 (5):1087-1123.
    In the context of modal logics one standardly considers two modal operators: possibility ) and necessity ) [see for example Chellas ]. If the classical negation is present these operators can be treated as inter-definable. However, negative modalities ) and ) are also considered in the literature [see for example Béziau ; Došen :3–14, 1984); Gödel, in: Feferman, Collected works, vol 1, Publications 1929–1936, Oxford University Press, New York, 1986, p. 300; Lewis and Langford ]. Both of them can be (...)
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  • A Note on the Issue of Cohesiveness in Canonical Models.Matteo Pascucci - 2020 - Journal of Logic, Language and Information 29 (3):331-348.
    In their presentation of canonical models for normal systems of modal logic, Hughes and Cresswell observe that some of these models are based on a frame which can be also thought of as a collection of two or more isolated frames; they call such frames ‘non-cohesive’. The problem of checking whether the canonical model of a given system is cohesive is still rather unexplored and no general decision procedure is available. The main contribution of this article consists in introducing a (...)
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  • Non-Boolean classical relevant logics I.Tore Fjetland Øgaard - 2019 - Synthese (8):1-32.
    Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic (...)
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  • Ontological Argument and Infinity in Spinoza’s Thought.J. L. Usó-Doménech, J. A. Nescolarde-Selva & Hugh Gash - 2020 - Foundations of Science 25 (2):385-400.
    If the words in Spinoza’s Ethics are considered as symbols, then certain words in the definitions of the Ethics can be replaced with symbols from set theory and we can reexamine Spinoza’s first definitions within a logical–mathematical frame. The authors believe that, some aspects of Spinoza’s work can be explained and illustrated through mathematics. A semantic relation between the definitions of the philosopher and set theory is presented. It is explained each chosen symbol. The ontological argument is developed through modal (...)
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  • Quantum Information Versus Epistemic Logic: An Analysis of the Frauchiger–Renner Theorem.Florian J. Boge - 2019 - Foundations of Physics 49 (10):1143-1165.
    A recent no-go theorem (Frauchiger and Renner in Nat Commun 9(1):3711, 2018) establishes a contradiction from a specific application of quantum theory to a multi- agent setting. The proof of this theorem relies heavily on notions such as ‘knows’ or ‘is certain that’. This has stimulated an analysis of the theorem by Nurgalieva and del Rio (in: Selinger P, Chiribella G (eds) Proceedings of the 15th international conference on quantum physics and logic (QPL 2018). EPTCS 287, Open Publishing Association, Waterloo, (...)
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  • Preface.Matteo Pascucci & Adam Tamas Tuboly - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):318-322.
    Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".
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  • Axiomatic and dual systems for constructive necessity, a formally verified equivalence.Lourdes del Carmen González-Huesca, Favio E. Miranda-Perea & P. Selene Linares-Arévalo - 2019 - Journal of Applied Non-Classical Logics 29 (3):255-287.
    We present a proof of the equivalence between two deductive systems for constructive necessity, namely an axiomatic characterisation inspired by Hakli and Negri's system of derivations from assumptions for modal logic , a Hilbert-style formalism designed to ensure the validity of the deduction theorem, and the judgmental reconstruction given by Pfenning and Davies by means of a natural deduction approach that makes a distinction between valid and true formulae, constructively. Both systems and the proof of their equivalence are formally verified (...)
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  • Vague Objects and Vague Identity: New Essays on Ontic Vagueness.Ken Akiba & Ali Abasnezhad (eds.) - 2014 - Dordrecht, Netherland: Springer.
    This unique anthology of new, contributed essays offers a range of perspectives on various aspects of ontic vagueness. It seeks to answer core questions pertaining to onticism, the view that vagueness exists in the world itself. The questions to be addressed include whether vague objects must have vague identity, and whether ontic vagueness has a distinctive logic, one that is not shared by semantic or epistemic vagueness. The essays in this volume explain the motivations behind onticism, such as the plausibility (...)
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  • Incompactness of the A1 Fragment of Basic Second Order Propositional Relevant Logic.Guillermo Badia - 2019 - Australasian Journal of Logic 16 (1):1-8.
    In this note we provide a simple proof of the incompactness over Routley-Meyer B-frames of the A1 fragment of the second order propositional relevant language.
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  • Intuitionism and the Modal Logic of Vagueness.Susanne Bobzien & Ian Rumfitt - 2020 - Journal of Philosophical Logic 49 (2):221-248.
    Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...)
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  • Mereology and time travel.Carlo Proietti & Jeroen Smid - 2020 - Philosophical Studies 177 (8):2245-2260.
    Core principles of mereology have been questioned by appealing to time travel scenarios. This paper questions the methodology of employing time travel scenarios to argue against mereology. We show some time travel scenarios are structurally equivalent to more standard ones not involving time travel; and that the three main theories about persistence through time can each solve both the time travel scenario as well as the structurally similar classical scenario. Time travel scenarios that are not similar to more standard arguments (...)
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  • Rosser Provability and Normal Modal Logics.Taishi Kurahashi - 2020 - Studia Logica 108 (3):597-617.
    In this paper, we investigate Rosser provability predicates whose provability logics are normal modal logics. First, we prove that there exists a Rosser provability predicate whose provability logic is exactly the normal modal logic \. Secondly, we introduce a new normal modal logic \ which is a proper extension of \, and prove that there exists a Rosser provability predicate whose provability logic includes \.
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  • A Logical Critique of Kant's Theory of Knowledge.Christian B. N. Gade - 2007 - Res Cogitans 4 (1).
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  • forall x: Calgary. An Introduction to Formal Logic (4th edition).P. D. Magnus, Tim Button, Robert Trueman, Richard Zach & Aaron Thomas-Bolduc - 2023 - Calgary: Open Logic Project.
    forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...)
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  • Modal validity and the dispensability of the actuality operator.Vittorio Morato - 2014 - In Michal Dancak & Vit Puncochar (eds.), The Logica Yearbook 2013.
    In this paper, I claim that two ways of defining validity for modal languages (“real-world” and “general” validity), corresponding to distinction between a correct and an incorrect way of defining modal valid- ity, correspond instead to two substantive ways of conceiving modal truth. At the same time, I claim that the major logical manifestation of the real- world/general validity distinction in modal propositional languages with the actuality operator should not be taken seriously, but simply as a by-product of the way (...)
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  • Validity and actuality.Vittorio Morato - 2014 - Logique Et Analyse 227:379-405.
    The notion of validity for modal languages could be defined in two slightly different ways. The first is the original definition given by S. Kripke, for which a formula φ of a modal language L is valid if and only if it is true in every actual world of every interpretation of L. The second is the definition that has become standard in most textbook presentations of modal logic, for which a formula φ of L is valid if and only (...)
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  • Two Kinds of Logical Impossibility.Alexander Sandgren & Koji Tanaka - 2020 - Noûs 54 (4):795-806.
    In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...)
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  • A New Framework for Epistemic Logic.Yanjing Wang - 2017 - In Proceedings of TARK 2017. EPTCS. pp. 515-534.
    Recent years witnessed a growing interest in non-standard epistemic logics of knowing whether, knowing how, knowing what, knowing why and so on. The new epistemic modalities introduced in those logics all share, in their semantics, the general schema of ∃x◻φ, e.g., knowing how to achieve φ roughly means that there exists a way such that you know that it is a way to ensure that φ. Moreover, the resulting logics are decidable. Inspired by those particular logics, in this work, we (...)
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  • Frontiers of Conditional Logic.Yale Weiss - 2019 - Dissertation, The Graduate Center, City University of New York
    Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...)
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  • Quantification and Epistemic Modality.Dilip Ninan - 2018 - Philosophical Review 127 (4):433-485.
    This essay introduces a puzzle about the interaction between quantifiers and epistemic modals. The puzzle motivates the idea that whether an object satisfies an epistemically modalized predicate depends on the mode of presentation of the domain of quantification. I compare two ways of implementing this idea, one using counterpart theory, the other using Aloni's 'conceptual covers' theory, and then provides some evidence in favor of the former.
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  • Rough Consequence and other Modal Logics.Martin Bunder - 2015 - Australasian Journal of Logic 12 (1).
    Chakraborty and Banerjee have introduced a rough consequence logic based on the modal logic S5. This paper shows that rough consequence logics, with many of the same properties, can be based on modal logics as weak as K, with a simpler formulation than that of Chakraborty and Banerjee. Also provided are decision procedures for the rough consequence logics and equivalences and independence relations between various systems S and the rough consequence logics, based on them. It also shows that each logic, (...)
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  • Factive knowability and the problem of possible omniscience.Jan Heylen - 2020 - Philosophical Studies 177 (1):65-87.
    Famously, the Church–Fitch paradox of knowability is a deductive argument from the thesis that all truths are knowable to the conclusion that all truths are known. In this argument, knowability is analyzed in terms of having the possibility to know. Several philosophers have objected to this analysis, because it turns knowability into a nonfactive notion. In addition, they claim that, if the knowability thesis is reformulated with the help of factive concepts of knowability, then omniscience can be avoided. In this (...)
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  • Modern Origins of Modal Logic.Roberta Ballarin - 2010 - Stanford Encyclopedia of Philosophy.
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  • Idealist Origins: 1920s and Before.Martin Davies & Stein Helgeby - 2014 - In Graham Oppy & Nick Trakakis (eds.), History of Philosophy in Australia and New Zealand. Dordrecht: Springer. pp. 15-54.
    This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...)
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  • A completeness theorem for continuous predicate modal logic.Stefano Baratella - 2019 - Archive for Mathematical Logic 58 (1-2):183-201.
    We study a modal extension of the Continuous First-Order Logic of Ben Yaacov and Pedersen :168–190, 2010). We provide a set of axioms for such an extension. Deduction rules are just Modus Ponens and Necessitation. We prove that our system is sound with respect to a Kripke semantics and, building on Ben Yaacov and Pedersen, that it satisfies a number of properties similar to those of first-order predicate logic. Then, by means of a canonical model construction, we get that every (...)
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  • Cosmological Arguments.Michael Almeida - 2018 - Cambridge University Press.
    The book discusses the structure, content, and evaluation of cosmological arguments. The introductory chapter investigates features essential to cosmological arguments. Traditionally, cosmological arguments are distinguished by their appeal to change, causation, contingency or objective becoming in the world. But none of these is in fact essential to the formulation of cosmological arguments. Chapters 1-3 present a critical discussion of traditional Thomistic, Kalam, and Leibnizian cosmological arguments, noting various advantages and disadvantages of these approaches. Chapter 4 offers an entirely new approach (...)
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  • Algebraization of Jaśkowski’s Paraconsistent Logic D2.Janusz Ciuciura - 2015 - Studies in Logic, Grammar and Rhetoric 42 (1):173-193.
    The aim of this paper is to present an algebraic approach to Jaśkowski’s paraconsistent logic D2. We present: a D2-discursive algebra, Lindenbaum- Tarski algebra for D2 and D2-matrices. The analysis is mainly based on the results obtained by Jerzy Kotas in the 70s.
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