• Degree-preserving Godel logics...

Treffer: Degree-preserving Godel logics with an involution: intermediate logics and (ideal) paraconsistency

Title:
Degree-preserving Godel logics with an involution: intermediate logics and (ideal) paraconsistency
Authors:
Coniglio, M. E., Esteva, F., Gispert, J., Godo, L.
Source:
Arieli, O., Zamansky, A. (eds), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, pp. 107-139. 2021. Cham: Springer
Publication Year:
2026
Subject Terms:
Logic in Computer Science, Logic, F.4.1, I.2.4
Document Type:
Report Working Paper
DOI:
10.1007/978-3-030-71258-7_6
Access URL:
http://arxiv.org/abs/2601.08474
Accession Number:
edsarx.2601.08474
Database:
arXiv

Weitere Informationen

In this paper we study intermediate logics between the degree preserving companion of Godel fuzzy logic with an involution and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts. Although these degree-preserving Godel logics are explosive with respect to Godel negation, they are paraconsistent with respect to the involutive negation. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between the degree-preserving n-valued Godel fuzzy logic with an involution and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued Lukasiewicz logics.
34 pages, 2 figures