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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…
While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…
Answer Set Programming (ASP) is a successful method for solving a range of real-world applications. Despite the availability of fast ASP solvers, computing answer sets demands a very large computational power, since the problem tackled is…
A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm,…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
Modal fixpoint logics traditionally play a central role in computer science, in particular in artificial intelligence and concurrency. The mu-calculus and its relatives are among the most expressive logics of this type. However, popular…
We use the connection between automata and logic to prove that a wide class of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first we generalize one of the central results in coalgebraic automata theory, namely…
This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally…
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
Even though modularity has been studied extensively in conventional logic programming, there are few approaches on how to incorporate modularity into Answer Set Programming, a prominent rule-based declarative programming paradigm. A major…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…
In this paper, a Gaifman-Shapiro-style module architecture is tailored to the case of Smodels programs under the stable model semantics. The composition of Smodels program modules is suitably limited by module conditions which ensure the…
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as…