Fully-Abstract Statecharts Semantics via Intuitionistic Kripke Models

Formula size games for modal logic and μ-calculus

Journal of Logic and Computation ◽

10.1093/logcom/exz025 ◽

2019 ◽

Vol 29 (8) ◽

pp. 1311-1344 ◽

Cited By ~ 2

Author(s):

Lauri T Hella ◽

Miikka S Vilander

Keyword(s):

Modal Logic ◽

Optimal Strategy ◽

Order Logic ◽

First Order Logic ◽

Kripke Models ◽

First Order ◽

Modal Operators ◽

Crucial Difference ◽

Definition Of ◽

Person Game

Abstract We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known Adler–Immerman game. However, due to a crucial difference in the definition of positions of the game, its winning condition is simpler, and the second player does not have a trivial optimal strategy. Thus, unlike the Adler–Immerman game, our game is a genuine two-person game. We illustrate the use of the game by proving a non-elementary succinctness gap between bisimulation invariant first-order logic $\textrm{FO}$ and (basic) modal logic $\textrm{ML}$. We also present a version of the game for the modal $\mu $-calculus $\textrm{L}_\mu $ and show that $\textrm{FO}$ is also non-elementarily more succinct than $\textrm{L}_\mu $.

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A Modal Semantics of Negation in Logic Programming

Fundamenta Informaticae ◽

10.3233/fi-1992-163-403 ◽

1992 ◽

Vol 16 (3-4) ◽

pp. 231-262

Author(s):

Philippe Balbiani

Keyword(s):

Modal Logic ◽

Logic Programming ◽

Modal Logics ◽

Kripke Models ◽

Logic Programs ◽

Modal Semantics ◽

Soundness And Completeness ◽

Modal Completion ◽

Well Foundedness

The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal completion formula. This formula is a modal translation of Clack’s formula. It gives soundness and completeness proofs for the negation as failure rule. It offers a formal characterization of unprovability in logic programs. It characterizes as well its stratified semantics.

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Weak Arithmetics and Kripke Models

Mathematical Logic Quarterly ◽

10.1002/1521-3870(200201)48:1<157::aid-malq157>3.0.co;2-3 ◽

2002 ◽

Vol 48 (1) ◽

pp. 157-160

Author(s):

Morteza Moniri

Keyword(s):

Kripke Models

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SEPARATING THE FAN THEOREM AND ITS WEAKENINGS

Journal of Symbolic Logic ◽

10.1017/jsl.2014.9 ◽

2014 ◽

Vol 79 (3) ◽

pp. 792-813 ◽

Cited By ~ 2

Author(s):

ROBERT S. LUBARSKY ◽

HANNES DIENER

Keyword(s):

Constructive Mathematics ◽

Kripke Models ◽

Fan Theorem

AbstractVarieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.

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