RT Journal Article
T1 Another paraconsistent algebraic semantics for Lukasiewicz-Pavelka logic
A1 Rodríguez, Juan Tinguaro
A1 Turunen, Esko
A1 Ruan, Da
A1 Montero, Javier
AB As recently proved in a previous work of Turunen, Tsoukias and Ozttirk, starting from an evidence pair (a, h) on the real unit square and associated with a propositional statement a, we can construct evidence matrices expressed in terms of four values t, f, k, u that respectively represent the logical valuations true, false, contradict ion (both true and false) and unknown (neither true nor false) regarding the statement a. The components of the evidence pair (a, h) are to be understood as evidence for and against a, respectively. Moreover, the set of all evidence matrices can be equipped with an injective MV-algebra structure. Thus, the set of evidence matrices can play the role of truth-values of a Lukasiewicz Pavelka fuzzy logic, a rich and applicable mathematical foundation for fuzzy reasoning, and in such a way that the obtained new logic is paraconsistent. In this paper we show that a similar result can be also obtained when the evidence pair (a, h) is given on the real unit triangle. Since the real unit triangle does not admit a natural MV-structure, we introduce some mathematical results to show how this shortcoming can be overcome, and another injective MV-algebra structure in the corresponding set of evidence matrices is obtained. Also, we derive several formulas to explicitly calculate the evidence matrices for the operations associated to the usual connectives.
PB Elsevier
SN 0165-0114
YR 2014
FD 2014-05-01
LK https://hdl.handle.net/20.500.14352/33574
UL https://hdl.handle.net/20.500.14352/33574
LA eng
NO Government of Spain
DS Docta Complutense
RD 19 may 2024