Qualitative choice logic (QCL) is a propositional logic for representing prioritized alternatives. The logic adds to classical propositional logic a new connective called ordered disjunction: A~×B intuitively means: if possible A, but if A is not possible then at least B. QCL inference is obtained by defining a preference relation between interpretations of a propositional language. This paper ...

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic ...

Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula in the language of inquisitive logic with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language of propositional dependence logic without these two connectives. We show that although such a (noncompositional) transl...

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorith...

We add propositional quantifiers to the propositional modal logic S4 and to the propositional intuitionsitic logic H, introducing axiom schemes that are the natural analogs to axiom schemes typically used for first-order quantifiers in classical logic. We show that the resulting logics are sound and complete for a topological semantics extending, in a natural way, the topological semantics for ...

We introduce a substructural propositional calculus of Sequential Dynamic Logic (SDL) that subsumes a propositional part of dynamic predicate logic (DPL), and is shown to be expressively equivalent to propositional dynamic logic (PDL). Completeness of the calculus with respect to the intended relational semantics is established.

In this paper it is shown that addition of certain reductions to the standard cut removing reductions of deductions in propositional logic makes propositional logic non-normalizable. From this follows that some provable propositions in propositional logic has no direct proof.

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values...

The two main founders of paraconsistent logic, Stanis law Jaśkowski and Newton da Costa, built their systems on distinct grounds. Starting from different projects, they used different tools and ultimately designed quite different calculi to attend their needs. How successful were their enterprises? Here we discuss the problem of defining paraconsistent logics following the original instructions...

We study quantified propositional logics from the complexity theoretic point of view. First we introduce alternating dependency quantified boolean formulae (ADQBF) which generalize both quantified and dependency quantified boolean formulae. We show that the truth evaluation for ADQBF is AEXPTIME(poly)-complete. We also identify fragments for which the problem is complete for the levels of the e...