scholarly journals A Note on the Complexity of the Satisfiability Problem for Graded Modal Logics

2009 ◽  
Author(s):  
Yevgeny Kazakov ◽  
Ian Pratt-Hartmann
Keyword(s):  
Modal Logics ◽  
Satisfiability Problem

scholarly journals Modal context restriction for multiagent BDI logics

2021 ◽  
Author(s):  
Marcin Dziubiński
Keyword(s):  
Multiagent Systems ◽  
Modal Logics ◽  
Satisfiability Problem ◽  
Language Restriction ◽  
Multimodal Logics ◽  
Fix Point

AbstractWe present and discuss a novel language restriction for modal logics for multiagent systems, called modal context restriction, that reduces the complexity of the satisfiability problem from EXPTIME complete to NPTIME complete. We focus on BDI multimodal logics that contain fix-point modalities like common beliefs and mutual intentions together with realism and introspection axioms. We show how this combination of modalities and axioms affects complexity of the satisfiability problem and how it can be reduced by restricting the modal context of formulas.

scholarly journals THE EXPRESSIVE POWER OF MEMORY LOGICS

2011 ◽  
Vol 4 (2) ◽  
pp. 290-318 ◽  
Author(s):  
CARLOS ARECES ◽  
DIEGO FIGUEIRA ◽  
SANTIAGO FIGUEIRA ◽  
SERGIO MERA
Keyword(s):  
Modal Logic ◽  
Expressive Power ◽  
Modal Logics ◽  
Hybrid Logic ◽  
Satisfiability Problem ◽  
Current Node

We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic ℋℒ (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.This work focuses in the case where the memory is a set, and we can test whether the current node belongs to the set or not. We prove that, in terms of expressive power, the memory logics we discuss here lie between the basic modal logic ${\cal K}$ and ℋℒ (↓). We show that the satisfiability problem of most of the logics we cover is undecidable. The only logic with a decidable satisfiability problem is obtained by imposing strong constraints on which elements can be memorized.

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 Simplest randomK-satisfiability problem

2001 ◽  
Vol 63 (2) ◽  
Author(s):  
Federico Ricci-Tersenghi ◽  
Martin Weigt ◽  
Riccardo Zecchina
Keyword(s):  
Satisfiability Problem

Unsatisfiable Core Analysis and Aggregates for Optimum Stable Model Search

2020 ◽  
Vol 176 (3-4) ◽  
pp. 271-297
Author(s):  
Mario Alviano ◽  
Carmine Dodaro
Keyword(s):  
State Of The Art ◽  
Answer Set Programming ◽  
Efficient Algorithms ◽  
Satisfiability Problem ◽  
Core Analysis ◽  
Stable Model ◽  
Maximum Satisfiability ◽  
Model Search ◽  
Unsatisfiable Core ◽  
Stable Models

Many efficient algorithms for the computation of optimum stable models in the context of Answer Set Programming (ASP) are based on unsatisfiable core analysis. Among them, algorithm OLL was the first introduced in the context of ASP, whereas algorithms ONE and PMRES were first introduced for solving the Maximum Satisfiability problem (MaxSAT) and later on adapted to ASP. In this paper, we present the porting to ASP of another state-of-the-art algorithm introduced for MaxSAT, namely K, which generalizes ONE and PMRES. Moreover, we present a new algorithm called OLL-IN-ONE that compactly encodes all aggregates of OLL by taking advantage of shared aggregate sets propagators. The performance of the algorithms have been empirically compared on instances taken from the latest ASP Competition.

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
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