Characterization Theorem of 4-valued De Morgan Logic
نویسندگان
چکیده
In this paper we give an axiom system of a non-linear 4-valued logic which we call a de Morgan logic (ML), whose Lindenbaum algebra is the de Morgan algebra with implication (MI-algebra), and show that (1) For every MI-algebra L, there is a quotient MI-algebra L such that it is embeddable to the simplest 4-valued MI-algebra M = {0, a, b, 1}; (2) The Lindenbaum algebra of ML is the MI-algebra; (3) The completeness theorem of ML is established; (4) ML is decidable.
منابع مشابه
Revisiting C1
We show that logic C1 cannot be extended to a paraconsistent logic in which the substitution theorem is valid. We show with the help of an answer set programming (ASP) tool called clasp, that C1 is robust with respect to certain three valued paraconsistent logics with some desirable properties. In particular C1 is robust with respect to three-valued logic P2, a logic for which some of the De Mo...
متن کاملAlternating Regular Tree Grammars in the Framework of Lattice-Valued Logic
In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued) regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is ta...
متن کاملClassical Negation and Expansions of Belnap-Dunn Logic
We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show th...
متن کاملPriestley duality for (modal) N4-lattices
N4-lattices are the algebraic semantics of paraconsistent Nelson logic, which was introduced in [1] as an inconsistency-tolerant counterpart of the better-known logic of Nelson [7, 13]. Paraconsistent Nelson logic combines interesting features of intuitionistic, classical and many-valued logics (e.g., Belnap-Dunn four-valued logic); recent work has shown that it can also be seen as one member o...
متن کاملχChek: A Model Checker for Multi-Valued Reasoning
This paper describes our multi-valued symbolic modelchecker χChek. χChek is a generalization of an existing symbolic model-checking algorithm for a multi-valued extension of the temporal logic CTL. Multi-valued modelchecking supports reasoning with values other than just TRUE and FALSE. Multi-valued logics are useful in software engineering because they support explicit modeling of uncertainty,...
متن کامل