Lukasiewicz Logic

Logics for belief functions on MV-algebras

Publication Type:

Journal Article

Authors:

Tommaso Flaminio; Lluís Godo; Enrico Marchioni

Source:

International Journal of Approximate Reasoning (0)

Keywords:

Belief Functions; Lukasiewicz Logic; Modal Logics; Fuzzy Events

Abstract:

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism.

Finite-valued Lukasiewicz modal logic is PSPACE-complete

Publication Type:

Conference Paper

Authors:

Fèlix Bou; Marco Cerami; Francesc Esteva

Source:

Twenty-second International Joint Conference on Artificial Intelligence (IJCAI 2011), Barcelona, p.774 - 779 (2011)

ISBN:

978-1-57735-516-8

Abstract:

It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either the Delta operator or truth constants in the language, i.e. in all these cases it is PSPACE- complete.

On Metric Temporal Lukasiewicz Logic

Publication Type:

Journal Article

Authors:

Tommaso Flaminio; Elisa B. P. Tiezzi

Source:

Electronic Notes in Theoretical Computer Science, Volume 246, p.71--85 (2009)

Keywords:

Metric Temporal Logic; Lukasiewicz Logic

Syndicate content