scholarly journals EVERYONE KNOWS THAT SOMEONE KNOWS: QUANTIFIERS OVER EPISTEMIC AGENTS

2019 ◽  
Vol 12 (2) ◽  
pp. 255-270 ◽  
Author(s):  
PAVEL NAUMOV ◽  
JIA TAO
Keyword(s):  
Modal Logic ◽  
Epistemic Logic ◽  
Possible Worlds ◽  
Completeness Theorem ◽  
Kripke Semantics ◽  
Possible Worlds Semantics ◽  
Distributed Knowledge ◽  
First Order ◽  
Soundness And Completeness ◽  
First Order Modal Logic

AbstractModal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.

A cut-free labelled sequent calculus for dynamic epistemic logic

2020 ◽  
Vol 30 (1) ◽  
pp. 321-348
Author(s):  
Shoshin Nomura ◽  
Hiroakira Ono ◽  
Katsuhiko Sano
Keyword(s):  
Modal Logic ◽  
Epistemic Logic ◽  
Sequent Calculus ◽  
Dynamic Epistemic Logic ◽  
Kripke Semantics ◽  
Cut Rule ◽  
Public Announcement ◽  
Public Announcement Logic ◽  
Soundness And Completeness ◽  
Labelled Sequent Calculus

Abstract Dynamic epistemic logic is a logic that is aimed at formally expressing how a person’s knowledge changes. We provide a cut-free labelled sequent calculus ($\textbf{GDEL}$) on the background of existing studies of Hilbert-style axiomatization $\textbf{HDEL}$ of dynamic epistemic logic and labelled calculi for public announcement logic. We first show that the $cut$ rule is admissible in $\textbf{GDEL}$ and show that $\textbf{GDEL}$ is sound and complete for Kripke semantics. Moreover, we show that the basis of $\textbf{GDEL}$ is extended from modal logic K to other familiar modal logics including S5 with keeping the admissibility of cut, soundness and completeness.

Prior’s Three-Valued Modal Logic Q and its Possible Applications

2007 ◽  
Vol 11 (1) ◽  
pp. 105-110
Author(s):  
Seiki Akama ◽  
◽  
Yasunori Nagata ◽  
Keyword(s):  
Modal Logic ◽  
Possible Worlds ◽  
Completeness Theorem ◽  
Kripke Semantics ◽  
Formal Properties

Prior proposed a three-valued modal logic Q as a “correct” modal logic from his philosophical motivations. Unfortunately, Prior’s Q and many-valued modal logic have been neglected in the tradition of many-valued and modal logic. In this paper, we introduce a version of three-valued Kripke semantics for Q, which aims to establish Prior’s ideas based on possible worlds. We investigate formal properties of Q and prove the completeness theorem of Q. We also compare our approach with others and suggest possible applications.

scholarly journals Set-Theoretic Dependence

2015 ◽  
Vol 12 (3) ◽  
Author(s):  
John Wigglesworth
Keyword(s):  
Modal Logic ◽  
Possible Worlds ◽  
Impossible Worlds ◽  
Logical Framework ◽  
Truth Conditions ◽  
First Order ◽  
Dependence Relations ◽  
Asymmetric Dependence ◽  
Satisfactory Account ◽  
First Order Modal Logic

In this paper, we explore the idea that sets depend on, or are grounded in, their members.  It is said that a set depends on each of its members, and not vice versa.  Members do not depend on the sets that they belong to.  We show that the intuitive modal truth conditions for dependence, given in terms of possible worlds, do not accurately capture asymmetric dependence relations between sets and their members.  We extend the modal truth conditions to include impossible worlds and give a more satisfactory account of  the dependence of a set on its members. Focusing on the case of singletons, we articulate a logical framework in which to evaluate set-theoretic dependence claims, using a normal first-order modal logic.  We show that on this framework the dependence of a singleton on its single members follows from logic alone. However, the converse does not hold.

scholarly journals Philosophical Issues from Kripke’s ‘Semantical Considerations on Modal Logic’

2016 ◽  
Vol 20 (1) ◽  
pp. 01
Author(s):  
John Divers
Keyword(s):  
Modal Logic ◽  
Possible Worlds ◽  
Ontological Commitment ◽  
Semantic Theory ◽  
Kripke Semantics ◽  
Crucial Importance ◽  
Possible Worlds Semantics ◽  
Philosophical Discussion ◽  
Modal Space ◽  
Clear Conception

http://dx.doi.org/10.5007/1808-1711.2016v20n1p1In ‘Semantical Considerations on Modal Logic’, Kripke articulates his project in the discourse of “possible worlds”. There has been much philosophical discussion of whether endorsement of the Kripke semantics brings ontological commitment to possible worlds. However, that discussion is less than satisfactory because it has been conducted without the necessary investigation of the surrounding philosophical issues that are raised by the Kripke semantics. My aim in this paper is to map out the surrounding territory and to commence that investigation. Among the surrounding issues, and my attitudes to them, are these: (1) the potential of the standard distinction between pure and impure versions of the semantic theory has been under-exploited; (2) there has been under-estimation of what is achieved by the pure semantic theory alone; (3) there is a methodological imperative to co-ordinate a clear conception of the purposes of the impure theory with an equally clear conception of the content the theory; (4) there is a need to support by argument claims about how such a semantic theory, even in an impure state, can fund explanations in the theory of meaning and metaphysics; (5) greater attention needs to be paid to the crucial advance that Kripke makes on the precursors of possible-worlds semantics proper (e.g. Carnap 1947) in clearly distinguishing variation across the worlds within a model of modal space from variation across such models and, finally, (6) the normative nature of the concept of applicability, of the pure semantic theory, is both of crucial importance and largely ignored.

Categories and Modalities

2018 ◽  
Author(s):  
Kohei Kishida
Keyword(s):  
Modal Logic ◽  
Category Theory ◽  
Kripke Semantics ◽  
Counterpart Theory ◽  
Stone Duality ◽  
Topological Semantics ◽  
First Order ◽  
Propositional Modal Logic ◽  
First Order Modal Logic

Category theory provides various guiding principles for modal logic and its semantic modeling. In particular, Stone duality, or “syntax-semantics duality”, has been a prominent theme in semantics of modal logic since the early days of modern modal logic. This chapter focuses on duality and a few other categorical principles, and brings to light how they underlie a variety of concepts, constructions, and facts in philosophical applications as well as the model theory of modal logic. In the first half of the chapter, I review the syntax-semantics duality and illustrate some of its functions in Kripke semantics and topological semantics for propositional modal logic. In the second half, taking Kripke’s semantics for quantified modal logic and David Lewis’s counterpart theory as examples, I demonstrate how we can dissect and analyze assumptions behind different semantics for first-order modal logic from a structural and unifying perspective of category theory. (As an example, I give an analysis of the import of the converse Barcan formula that goes farther than just “increasing domains”.) It will be made clear that categorical principles play essential roles behind the interaction between logic, semantics, and ontology, and that category theory provides powerful methods that help us both mathematically and philosophically in the investigation of modal logic.

scholarly journals Neighborhood-Sheaf Semantics for First-Order Modal Logic

2011 ◽  
Vol 278 ◽  
pp. 129-143 ◽  
Author(s):  
Kohei Kishida
Keyword(s):  
Modal Logic ◽  
First Order ◽  
First Order Modal Logic

scholarly journals TOPOLOGY AND MODALITY: THE TOPOLOGICAL INTERPRETATION OF FIRST-ORDER MODAL LOGIC

2008 ◽  
Vol 1 (02) ◽  
Author(s):  
STEVE AWODEY ◽  
KOHEI KISHIDA
Keyword(s):  
Modal Logic ◽  
First Order ◽  
Topological Interpretation ◽  
First Order Modal Logic

Language, Meaning, and Information

2014 ◽  
Author(s):  
Scott Soames
Keyword(s):  
Modal Logic ◽  
Philosophy Of Language ◽  
Possible Worlds ◽  
Philosophy Of Mathematics ◽  
Scientific Study ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Possible Worlds Semantics ◽  
Language Meaning

This chapter is a case study of the process by which the attempt to solve philosophical problems sometimes leads to the birth of new domains of scientific inquiry. It traces how advances in logic and the philosophy of mathematics, starting with Gottlob Frege and Bertrand Russell, provided the foundations for what became a rigorous and scientific study of language, meaning, and information. After sketching the early stages of the story, it explains the importance of modal logic and “possible worlds semantics” in providing the foundation for the last half century of work in linguistic semantics and the philosophy of language. It argues that this foundation is insufficient to support the most urgently needed further advances. It proposes a new conception of truth-evaluable information as inherently representational cognitive acts of certain kinds. The chapter concludes by explaining how this conception of propositions can be used to illuminate the notion of truth; vindicate the connection between truth and meaning; and fulfill a central, but so far unkept, promise of possible worlds semantics.

Logical Tools

2021 ◽  
pp. 14-52
Author(s):  
Cian Dorr ◽  
John Hawthorne ◽  
Juhani Yli-Vakkuri
Keyword(s):  
Modal Logic ◽  
Possible Worlds ◽  
Higher Order ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
System P

This chapter presents the system of classical higher-order modal logic which will be employed throughout this book. Nothing more than a passing familiarity with classical first-order logic and standard systems of modal logic is presupposed. We offer some general remarks about the kind of commitment involved in endorsing this logic, and motivate some of its more non-standard features. We also discuss how talk about possible worlds can be represented within the system.

First-Order Modal Logic

1998 ◽  
Author(s):  
Melvin Fitting ◽  
Richard L. Mendelsohn
Keyword(s):  
Modal Logic ◽  
First Order ◽  
First Order Modal Logic
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