Compactness of first-order fuzzy logics
Abstract
One of the nice properties of the first-order logic is the compactness of satisfiability. It state that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in many-valued logics, poses various kind of the compactness in these logics. One of this issues is the compactness of $K$-satisfiability. Here, after an overview on the results around the compactness of satisfiability and compactness of $K$-satisfiability in many-valued logic based on continuous t-norms (basic logic), we extend the results around this topic. To this end, we consider a reverse semantical meaning for basic logic. Then we introduce a topology on $[0,1]$ and $[0,1]^2$ that the interpretation of all logical connectives are continuous with respect to these topologies. Finally using this fact we extend the results around the compactness of satisfiability in basic ogic.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.01441
- arXiv:
- arXiv:1905.01441
- Bibcode:
- 2019arXiv190501441K
- Keywords:
-
- Mathematics - Logic;
- 03b50;
- 03c20;
- 03g10
- E-Print:
- Iranian Journal of Fuzzy Systems, Volume 19, Number 3, (2022), pp. 53-68