Melvin Fitting and Richard L. Mendelsohn. First-order modal logic. Synthese library, vol. 277. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1998, xii + 287 pp.

2002 ◽  
Vol 8 (3) ◽  
pp. 429-431
Author(s):  
Roderic A. Girle
Keyword(s):  
Modal Logic ◽  
First Order ◽  
First Order 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

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.

First-Order Modal Logic

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

scholarly journals ERRATUM

2008 ◽  
Vol 1 (3) ◽  
pp. 393-393
Keyword(s):  
Modal Logic ◽  
Production Process ◽  
Symbolic Logic ◽  
First Order ◽  
Topological Interpretation ◽  
Final Equation ◽  
First Order Modal Logic

Steve Awodey and Kohei Kishida (2008). Topology and Modality: The Topological Interpretation of First-Order Modal Logic. The Review of Symbolic Logic 1(2): 146-166.On page 148 of this article an error was introduced during the production process. The final equation in the displayed formula 8 lines from the bottom of the page should read,[0, 1) ≠ [0, 1]The publisher regrets this error.

scholarly journals First-order modal logic in the necessary framework of objects

2016 ◽  
Vol 46 (4-5) ◽  
pp. 584-609 ◽  
Author(s):  
Peter Fritz
Keyword(s):  
Modal Logic ◽  
Model Theory ◽  
Consequence Relations ◽  
Possible World ◽  
Logical Constants ◽  
First Order ◽  
Timothy Williamson ◽  
Infinite Sets ◽  
Infinite Set ◽  
First Order Modal Logic

AbstractI consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson's argument.

On the expressive power of first-order modal logic with two-dimensional operators

Synthese ◽  
2016 ◽  
Vol 195 (10) ◽  
pp. 4373-4417 ◽  
Author(s):  
Alexander W. Kocurek
Keyword(s):  
Modal Logic ◽  
Expressive Power ◽  
Two Dimensional ◽  
First Order ◽  
First Order Modal Logic

scholarly journals An Arithmetically Complete Predicate Modal Logic

2021 ◽  
Author(s):  
George Tourlakis ◽  
Yunge Hao
Keyword(s):  
Modal Logic ◽  
Current Paper ◽  
Kripke Models ◽  
First Order ◽  
Semantic Completeness ◽  
First Order Modal Logic ◽  
Conservation Theorem ◽  
Order Extension

This paper investigates a first-order extension of GL called \(\textup{ML}^3\). We outline briefly the history that led to \(\textup{ML}^3\), its key properties and some of its toolbox: the \emph{conservation theorem}, its cut-free Gentzenisation, the ``formulators'' tool. Its semantic completeness (with respect to finite reverse well-founded Kripke models) 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 \(\textup{ML}^3\) is arithmetically complete. As expanded below, \(\textup{ML}^3\) is a first-order modal logic that along with its built-in ability to simulate general classical first-order provability―"\(\Box\)" simulating the the informal classical "\(\vdash\)"―is also arithmetically complete in the Solovay sense.

The Fitch-Church Paradox and First Order Modal Logic

Erkenntnis ◽  
2015 ◽  
Vol 81 (1) ◽  
pp. 87-104
Author(s):  
Carlo Proietti
Keyword(s):  
Modal Logic ◽  
First Order ◽  
First Order Modal Logic
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