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.

ON THE PROPOSITIONAL SLDNF-RESOLUTION

1996 ◽  
Vol 07 (04) ◽  
pp. 359-406 ◽  
Author(s):  
JAN A. PLAZA
Keyword(s):  
Propositional Logic ◽  
Modal Logics ◽  
Logic Programs ◽  
Negation As Failure ◽  
Intermediate Logics ◽  
Original Program ◽  
Declarative Semantics ◽  
Constructive Version ◽  
Fix Point ◽  
Multivalued Semantics

We consider propositional logic programs with negations. We define notions of constructive transformation and constructive completion of a program. We use these notions to characterize SLDNF-resolution in classical, intuitionistic and intermediate logics, and also to derive a characterization in modal logics of knowledge. We show that the three-valued and four-valued fix-point or declarative semantics for program P are equivalent to the two-valued semantics for the constructive version of P. We argue that it would be beneficial to replace Negation as Failure by constructive transformation, and it would be beneficial to use the semantics for the constructive version of the program instead of multivalued semantics for the original program.

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.

Modifier Logics Based on Graded Modalities

2003 ◽  
Vol 7 (2) ◽  
pp. 72-78 ◽  
Author(s):  
Jorma K. Mattila ◽  
Keyword(s):  
Modal Logics ◽  
Formal Semantic ◽  
Fuzzy Topology ◽  
Topological Semantics ◽  
Modal Operators ◽  
Operator Systems ◽  
Multimodal Logics ◽  
Interior Operator ◽  
Graded Modalities

Modifier logics are considered as generalizations of "classical" modal logics. Thus modifier logics are so-called multimodal logics. Multimodality means here that the basic logics are modal logics with graded modalities. The interpretation of modal operators is more general, too. Leibniz’s motivating semantical ideas (see [8], p. 20-21) give justification to these generalizations. Semantics of canonical frames forms the formal semantic base for modifier logics. Several modifier systems are given. A special modifier calculus is combined from some "pure" modifier logics. Creating a topological semantics to this special modifier logic may give a basis to some kind of fuzzy topology. Modifier logics of S4-type modifiers will give a graded topological interior operator systems, and thus we have a link to fuzzy topology.

Modal Logics for Reasoning about Multiagent Systems

2011 ◽  
pp. 1089-1094
Author(s):  
Nikolay V. Shilov ◽  
Natalia Garanina
Keyword(s):  
Modal Logic ◽  
Multiagent Systems ◽  
Dynamic Logic ◽  
Modal Logics ◽  
Kripke Models ◽  
Linear Orders ◽  
Propositional Dynamic Logic ◽  
Combined Logics ◽  
Logic Of Knowledge ◽  
Scientific Context

It becomes evident in recent years a surge of interest to applications of modal logics for specification and validation of complex systems. It holds in particular for combined logics of knowledge, time and actions for reasoning about multiagent systems (Dixon, Nalon & Fisher, 2004; Fagin, Halpern, Moses & Vardi, 1995; Halpern & Vardi, 1986; Halpern, van der Meyden & Vardi, 2004; van der Hoek & Wooldridge, 2002; Lomuscio, & Penczek, W., 2003; van der Meyden & Shilov, 1999; Shilov, Garanina & Choe, 2006; Wooldridge, 2002). In the next paragraph we explain what are logics of knowledge, time and actions from a viewpoint of mathematicians and philosophers. It provides us a historic perspective and a scientific context for these logics. For mathematicians and philosophers logics of actions, time, and knowledge can be introduced in few sentences. A logic of actions (ex., Elementary Propositional Dynamic Logic (Harel, Kozen & Tiuryn, 2000)) is a polymodal variant of a basic modal logic K (Bull & Segerberg, 2001) to be interpreted over arbitrary Kripke models. A logic of time (ex., Linear Temporal Logic (Emerson, 1990)) is a modal logic with a number of modalities that correspond to “next time”, “always”, “sometimes”, and “until” to be interpreted in Kripke models over partial orders (discrete linear orders for LTL in particular). Finally, a logic of knowledge or epistemic logic (ex., Propositional Logic of Knowledge (Fagin, Halpern, Moses & Vardi, 1995; Rescher, 2005)) is a polymodal variant of another basic modal logic S5 (Bull & Segerberg, 2001) to be interpreted over Kripke models where all binary relations are equivalences.

Co-evolution of Hetero Multiagent Systems using Genetic Network Programming.

2003 ◽  
Vol 123 (3) ◽  
pp. 544-551 ◽  
Author(s):  
Kotaro Hirasawa ◽  
Masafumi Okubo ◽  
Jinglu Hu ◽  
Junichi Murata ◽  
Yuko Matsuya
Keyword(s):  
Multiagent Systems ◽  
Genetic Network ◽  
Network Programming ◽  
Genetic Network Programming
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