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Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…

Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…

The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…

This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator…

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…

We present alternative definitions of the first-order stable model semantics and its extension to incorporate generalized quantifiers by referring to the familiar notion of a reduct instead of referring to the SM operator in the original…

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…

In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to…

We define a framework for incorporating alternation-free fixpoint logics into the dual-adjunction setup for coalgebraic modal logics. We achieve this by using order-enriched categories. We give a least-solution semantics as well as an…

This paper analyses the declarative readings of logic programming. Logic programming - and negation as failure - has no unique declarative reading. One common view is that logic programming is a logic for default reasoning, a sub-formalism…

Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…

In this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define…

An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…

We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…

We establish a novel relation between delete-free planning, an important task for the AI Planning community also known as relaxed planning, and logic programming. We show that given a planning problem, all subsets of actions that could be…

Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective…

Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to…

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…