Related papers: Normal forms for Answer Sets Programming
An answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
The arithmetic of natural numbers has a natural and simple encoding within sets, and the simplest set whose structure is not that of any natural number extends this set-theoretic representation to positive and negative integers. The…
We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
In this paper, we investigate the fundamental laws of quantum programming. We extend a comprehensive set of Hoare et al.'s basic laws of classical programming to the quantum setting. These laws characterise the algebraic properties of…
We present an explanation system for applications that leverage Answer Set Programming (ASP). Given a program P, an answer set A of P, and an atom a in the program P, our system generates all explanation graphs of a which help explain why a…
This paper describes a generalization of Clark's completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to…
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…
A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems…
Formal logic enables computers to reason in natural language by representing sentences in symbolic forms and applying rules to derive conclusions. However, in what our study characterizes as "rulebreaker" scenarios, this method can lead to…
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…
In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a…
We investigate mca-programs, that is, logic programs with clauses built of monotone cardinality atoms of the form kX, where k is a non-negative integer and X is a finite set of propositional atoms. We develop a theory of mca-programs. We…
Most controlled natural languages (CNLs) are processed with the help of a pipeline architecture that relies on different software components. We investigate in this paper in an experimental way how well answer set programming (ASP) is…
Every definite logic program has as its meaning a least Herbrand model with respect to the program-independent ordering "set-inclusion". In the case of normal logic programs there do not exist least models in general. However, according to…
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,…
The rules associated with propositional logic programs and the stable model semantics are not expressive enough to let one write concise programs. This problem is alleviated by introducing some new types of propositional rules. Together…
Answer set programming (ASP) is a logic programming formalism used in various areas of artificial intelligence like combinatorial problem solving and knowledge representation and reasoning. It is known that enhancing ASP with function…
Our main contribution is to show that the behaviour of kernels across multiple layers of a convolutional neural network can be approximated using a logic program. The extracted logic programs yield accuracies that correlate with those of…