Representation of knowledge and uncertainty in temporal logic LTL with since on frames Z of integer numbers

Authors:
Vladimir V. Rybakov
Affiliations:
School of Computing, Mathematics and IT, Manchester Metropolitan University, Manchester, UK and Institutes of Mathematics, Siberian Federal University, Krasonoyarsk, Russia
Venue:
KES'11 Proceedings of the 15th international conference on Knowledge-based and intelligent information and engineering systems - Volume Part I
Year:
2011

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Abstract

We study a new hybrid logic LT LIAZ,U using as components: LTL based on Z with operations Since and Previous, multi-agent logic with interacting agents, and operation of logical uncertainty. The language of LTLIAZ,U contains, together with the standard operations of LTL and multi-agent logic, new knowledge operations KnI (for 'known through interaction'), GKL and GKG (for local and global general knowledge), and expressible logical operations: U - for uncertainty, and Ul for local uncertainty. We consider questions of satisfiability and decidability for LTLIAZ,U. The key result is construction of an algorithm which recognizes theorems of LTLIAZ,U (this implies that LTLIAZ,U is decidable, and the satisfiability problem for LTLIAZ,U is solvable).