Tree-Like Proof Systems for Finitely-Many Valued Non-deterministic Consequence Relations

Proof Theories for Some Prioritized Consequence Relations

Handling a possibly inconsistent prioritized belief base can be done in terms of consistent subsets. Humans do not compute consistent subsets, they just start reasoning and when confronted with inconsistencies in the course of their reasoning, they may adjust their interpretation of the information. In logics this behaviour corresponds to the mechanisms of dynamic proof theories. The aim of thi...

Transporting many-valued sets along many-valued relations

The transport of L-sets along an L-relation R is considered, with L any residuated lattice, sometimes with further properties as to be a frame or an MV-algebra. Pairs of powerset operators related to R are considered and their basic properties are studied in a comprehensive discussion including some results already known. A few examples and suggestions for application and further development ar...

Some rank equalities for finitely many tripotent matrices

‎A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations‎. ‎Moreover‎, ‎by using this equality and Theorems 8 and 10 in [Chen M‎. ‎and et al‎. ‎On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications‎, ‎The Scientific World Journal 2014 (2014)‎, ‎Article ID 702413‎, ‎7 page...

Non-deterministic Multiple-valued Structures

Studying Sequent Systems via Non-deterministic Multiple-Valued Matrices

We consider a family of sequent systems with “well-behaved” logical rules in which the cut rule and/or the identity-axiom are not present. We provide a semantic characterization of the logics induced by these systems in the form of non-deterministic three-valued or four-valued matrices. The semantics is used to study some important proof-theoretic properties of these systems. These results shed...