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We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way,…

We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…

Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…

We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…

We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…

An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that "logic programs" are not about logic but constitute inductive definitions of sets and relations. A skeletal language design…

There are various interesting semantics' (extensions) designed for argumentation frameworks. They enable to assign a meaning, e.g., to odd-length cycles. Our main motivation is to transfer semantics' proposed by Baroni, Giacomin and Guida…

This note is about the relationship between two theories of negation as failure -- one based on program completion, the other based on stable models, or answer sets. Francois Fages showed that if a logic program satisfies a certain…

Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…

A systematic algebraic framework for composing and decomposing logic programs is currently missing, limiting our ability to analyze and construct programs in a modular way. In this paper, we introduce set-like operations for (propositional…

Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…

The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…

Belief revision has been studied mainly with respect to background logics that are monotonic in character. In this paper we study belief revision when the underlying logic is non-monotonic instead--an inherently interesting problem that is…

This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…

We apply proof-theoretic techniques in answer Set Programming. The main results include: 1. A characterization of continuity properties of Gelfond-Lifschitz operator for logic program. 2. A propositional characterization of stable models of…

In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…