A New Representation Theorem for Many-valued Modal Logics

We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the Kripke possible-world semantics for it. Such a new framework offers a new semantics for many-valued logics based on the truth-invariance entailment. Consequently, it is substantially different from current definitions based on a matrix with a designated subset of logic values, used for the satisfaction relation, often difficult to fix. In the case when the many-valued modal logics are based on the set of truthvalues that are complete distributive lattices we obtain a compact autoreferential Kripke-style canonical representation. The Kripke-style semantics for this subclass of modal logics have the joint-irreducible subset of the carrier set of many-valued algebras as set of possible worlds. A significant member of this subclass is the paraconsis...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Zoran Majkic
• Keywords: CORR 2011, Distributive Lattices, Education, Modal Logics, World Semantics