ON NON FINITE AXIOMATIZABILITY OF n-MODAL LOGICS BETWEEN AND FOR FINITE

2020 ◽  
Vol 47 (1) ◽  
pp. 99-119
Author(s):  
Tarek Sayed Ahmed
Keyword(s):  
Modal Logics ◽  
Finite Axiomatizability

scholarly journals On the multi-dimensional modal logic of substitutions

2019 ◽  
Vol 56 (4) ◽  
pp. 454-481
Author(s):  
Tarek Sayed Ahmed ◽  
Mohammad Assem Mahmoud
Keyword(s):  
Amalgamation Property ◽  
Modal Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Kripke Semantics ◽  
Infinite Dimensions ◽  
Finite Axiomatizability ◽  
First Order ◽  
Abstract Entities ◽  
Omitting Types

Abstract We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an N P complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability.

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values

scholarly journals On modal logics arising from scattered locally compact Hausdorff spaces

2019 ◽  
Vol 170 (5) ◽  
pp. 558-577
Author(s):  
Guram Bezhanishvili ◽  
Nick Bezhanishvili ◽  
Joel Lucero-Bryan ◽  
Jan van Mill
Keyword(s):  
Modal Logics ◽  
Hausdorff Spaces ◽  
Locally Compact

Modal logics of domains on the real plane

Studia Logica ◽  
1983 ◽  
Vol 42 (1) ◽  
pp. 63-80 ◽  
Author(s):  
V. B. Shehtman
Keyword(s):  
Modal Logics ◽  
Real Plane ◽  
The Real

Analyzing completeness of axiomatic functional systems for temporal × modal logics

2010 ◽  
Vol 56 (1) ◽  
pp. 89-102 ◽  
Author(s):  
Alfredo Burrieza ◽  
Inmaculada P. de Guzmán ◽  
Emilio Muñoz-Velasco
Keyword(s):  
Modal Logics ◽  
Functional Systems

A Modal Semantics of Negation in Logic Programming

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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