Completeness Theorems for $$\exists \Box $$-Fragment of 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.

Download Full-text

First-Order Modal Logic

10.1007/978-94-011-5292-1 ◽

1998 ◽

Cited By ~ 177

Author(s):

Melvin Fitting ◽

Richard L. Mendelsohn

Keyword(s):

Modal Logic ◽

First Order ◽

First Order Modal Logic

Download Full-text

ERRATUM

The Review of Symbolic Logic ◽

10.1017/s175502030808026x ◽

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.

Download Full-text

First-order modal logic in the necessary framework of objects

Canadian Journal of Philosophy ◽

10.1080/00455091.2015.1132976 ◽

2016 ◽

Vol 46 (4-5) ◽

pp. 584-609 ◽

Cited By ~ 4

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.

Download Full-text