Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between output predicates and auxiliary predicates. For tight programs, that generalization of completion is known to match the stable model semantics, which is the basis of answer set programming. We show that the tightness condition in this theorem can be replaced by a less restrictive “local tightness” requirement. From this fact we conclude that the proof assistant anthem-p2p can be used to verify equivalence between locally tight programs.

We propose a method for generating rule sets as global and local explanations for tree-ensemble learning methods using answer set programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in the construction of rules, which in turn are assessed using pattern mining methods encoded in ASP to extract explanatory rules. For global explanations, candidate rules are chosen from the entire trained tree-ensemble models, whereas for local explanations, candidate rules are selected by only considering rules that are relevant to the particular predicted instance. We show how user-defined constraints and preferences can be represented declaratively in ASP to allow for transparent and flexible rule set generation, and how rules can be used as explanations to help the user better understand the models. Experimental evaluation with real-world datasets and popular tree-ensemble algorithms demonstrates that our approach is applicable to a wide range of classification tasks.

This technical note shows how we have combined prescriptive type checking and constraint solving to increase automation during software verification. We do so by defining a type system and implementing a typechecker for $\{log\}$ (read ‘setlog’), a Constraint Logic Programming language and satisfiability solver based on set theory. The constraint solver is proved to be safe w.r.t. the type system. Two industrial-strength case studies are presented where this combination is used with very good results.

This note presents a historical survey of informal semantics that are associated with logic programming under answer set semantics. We review these in uniform terms and align them with two paradigms: Answer Set Programming and ASP-Prolog — two prominent Knowledge Representation and Reasoning Paradigms in Artificial Intelligence.

Static analysis of logic programs by abstract interpretation requires designing abstract operators which mimic the concrete ones, such as unification, renaming, and projection. In the case of goal-driven analysis, where goal-dependent semantics are used, we also need a backward-unification operator, typically implemented through matching. In this paper, we study the problem of deriving optimal abstract matching operators for sharing and linearity properties. We provide an optimal operator for matching in the domain $\mathtt{ShLin}^{\omega }$, which can be easily instantiated to derive optimal operators for the domains $\mathtt{ShLin}^2$ by Andy King and the reduced product $\mathtt{Sharing} \times \mathtt{Lin}$.