| Logical inference starts with concluding that if B implies A, and B is true, then A is true as well. To describe probabilistic inference rules, we must therefore deene the probability of an implication \A if B". There exist two diierent approaches to deening this probability, and these approaches lead to diierent probabilistic inference rules: We may interpret the probability of an implicatio...

Matthew Spinks [35] introduces implicative BCSK-algebras, expanding implicative BCK-algebras with an additional binary operation. Subdirectly irreducible implicative BCSK-algebras can be viewed as flat posets with two operations coinciding only in the 1and 2-element cases, each, in the latter case, giving the two-valued implication truth-function. We introduce the resulting logic (for the gener...

We investigate the application of Courcelle’s Theorem and the logspace version of Elberfeld et al. in the context of the implication problem for propositional sets of formulae, the extension existence problem for default logic, as well as the expansion existence problem for autoepistemic logic and obtain fixed-parameter time and space efficient algorithms for these problems. On the other hand, ...

Reasoning about preferences is a major issue in many decision making problems. Recently, a new logic for handling preferences, called Qualitative Choice Logic (QCL), was presented. This logic adds to classical propositional logic a new connective, called ordered disjunction symbolized by ×. That new connective is used to express preferences between alternatives. QCL was not designed to handle c...

The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to formalize the logic of Reverse Mathematics into a system that we name s-logic. We argue that s-logic captures precisely the “logical” content of the implication...

Quasi-Nelson logic is a recently-introduced generalization of Nelson’s constructive with strong negation to non-involutive setting. In the present paper we axiomatize negation-implication fragment quasi-Nelson (QNI-logic), which constitutes in sense algebraizable core logic. We introduce finite Hilbert-style calculus for QNI-logic, showing completeness and algebraizability respect variety QNI-al...