This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large.

In everyday life it happens that a person has to reason out what other peoplethink and how they behave, in order to achieve his goals. In other words, anindividual may be required to adapt his behavior by reasoning about the others'mental state. In this paper we focus on a knowledge-representation languagederived from logic programming which both supports the representation of mentalstates of individual communities and provides each with the capability ofreasoning about others' mental states and acting accordingly. The proposedsemantics is shown to be translatable into stable model semantics of logicprograms with aggregates.

Assertion checking is an invaluable programmer’s tool for finding many classes of errors or verifying their absence in dynamic languages such as Prolog. For Prolog programmers, this means being able to have relevant properties, such as modes, types, determinacy, nonfailure, sharing, constraints, and cost, checked and errors flagged without having to actually run the program. Such global static analysis tools are arguably most useful the earlier they are used in the software development cycle, and fast response times are essential for interactive use. Triggering a full and precise semantic analysis of a software project every time a change is made can be prohibitively expensive. This is specially the case when complex properties need to be inferred for large, realistic code bases. In our static analysis and verification framework, this challenge is addressed through a combination of modular and incremental (context- and path-sensitive) analysis that is responsive to program edits, at different levels of granularity. In this tool paper, we present how the combination of this framework within an integrated development environment (IDE) takes advantage of such incrementality to achieve a high level of reactivity when reflecting analysis and verification results back as colorings and tooltips directly on the program text – the tool’s VeriFly mode. The concrete implementation that we describe is Emacs-based and reuses in part off-the-shelf “on-the-fly” syntax checking facilities (flycheck). We believe that similar extensions are also reproducible with low effort in other mature development environments. Our initial experience with the tool shows quite promising results, with low latency times that provide early, continuous, and precise assertion checking and other semantic feedback to programmers during the development process. The tool supports Prolog natively, as well as other languages by semantic transformation into Horn clauses.

In Constraint Programming, a portfolio solver combines a variety of different constraint solvers for solving a given problem. This fairly recent approach enables to significantly boost the performance of single solvers, especially when multicore architectures are exploited. In this work, we give a brief overview of the portfolio solver sunny-cp, and we discuss its performance in the MiniZinc Challenge—the annual international competition for Constraint Programming solvers—where it won two gold medals in 2015 and 2016.

In the analysis of logic programs, abstract domains for detecting sharing properties are widely used. Recently, the new domain ${\mathtt{ShLin}^{\omega}}$ has been introduced to generalize both sharing and linearity information. This domain is endowed with an optimal abstract operator for single-binding unification. The authors claim that the repeated application of this operator is also optimal for multibinding unification. This is the proof of such a claim.

This paper presents a language, Alda, that supports all of logic rules, sets, functions, updates, and objects as seamlessly integrated built-ins. The key idea is to support predicates in rules as set-valued variables that can be used and updated in any scope, and support queries using rules as either explicit or implicit automatic calls to an inference function. We have defined a formal semantics of the language, implemented a prototype compiler that builds on an object-oriented language that supports concurrent and distributed programming and on an efficient logic rule system, and successfully used the language and implementation on benchmarks and problems from a wide variety of application domains. We describe the compilation method and results of experimental evaluation.

Head-elementary-set-free (HEF) programs were proposed in (Gebser et al. 2007) and shown to generalize over head-cycle-free programs while retaining their nice properties. It was left as an open problem in (Gebser et al. 2007) to establish the complexity of identifying HEF programs. This note solves the open problem by showing that the problem is complete for coNP.

In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.

Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far from immediate to verify whether a program that is claimed to be inconsistent, indeed does not admit any answer sets. In this paper, we address this problem and develop the new proof format ASP-DRUPE for propositional, disjunctive logic programs, including weight and choice rules. ASP-DRUPE is based on the Reverse Unit Propagation (RUP) format designed for Boolean satisfiability. We establish correctness of ASP-DRUPE and discuss how to integrate it into modern ASP solvers. Later, we provide an implementation of ASP-DRUPE into the wasp solver for normal logic programs.

Logic programming provides a high-level view of programming, giving implementers a vast latitude into what techniques to explore to achieve the best performance for logic programs. Towards obtaining maximum performance, one of the holy grails of logic programming has been to design computational models that could be executed efficiently and that would allow both for a reduction of the search space and for exploiting all the available parallelism in the application. These goals have motivated the design of the Extended Andorra Model (EAM), a model where goals that do not constrain nondeterministic goals can execute first. In this work, we present and evaluate the Basic design for EAM, a system that builds upon David H. D. Warren's original EAM with Implicit Control. We provide a complete description and implementation of the Basic design for EAM System as a set of rewrite and control rules. We present the major data structures and execution algorithms that are required for efficient execution, and evaluate system performance. A detailed performance study of our system is included. Our results show that the system achieves acceptable base performance and that a number of applications benefit from the advanced search inherent to the EAM.

Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP($\mathcal A \mathcal C$)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs. While undecidable in general, expressive fragments of ASP($\mathcal A \mathcal C$) can be exploited for effective problem solving in a rich framework.

We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be modular, in the sense that they also work if applied only to part of a theory, in order to achieve a useful notion of relative expressiveness. We present simulations showing that logics in DL with and without the capability of team defeat are equally expressive. We also show that logics that handle ambiguity differently – ambiguity blocking versus ambiguity propagating – have distinct expressiveness, with neither able to simulate the other under a different formulation of expressiveness.

A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson’s strong negation.

Recent work has provided delimited control for Prolog to dynamically manipulate the program control-flow, and to implement a wide range of control-flow and dataflow effects on top of. Unfortunately, delimited control is a rather primitive language feature that is not easy to use.

As a remedy, this work introduces algebraic effect handlers for Prolog, as a high-level and structured way of defining new side-effects in a modular fashion. We illustrate the expressive power of the feature and provide an implementation by means of elaboration into the delimited control primitives.

The latter add a non-negligible performance overhead when used extensively. To address this issue, we present an optimised compilation approach that combines partial evaluation with dedicated rewrite rules. The rewrite rules are driven by a lightweight effect inference that analyses what effect operations may be called by a goal. We illustrate the effectiveness of this approach on a range of benchmarks.

The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O([mid ]At(P)[mid ] × size(P)) steps, where size(P) denotes the total number of occurrences of atoms in a logic program P. This bound is achieved by an algorithm introduced by Van Gelder and known as the alternating-fixpoint algorithm. Improving on the alternating-fixpoint algorithm turned out to be difficult. In this paper we study extensions and modifications of the alternating-fixpoint approach. We then restrict our attention to the class of programs whose rules have no more than one positive occurrence of an atom in their bodies. For programs in that class we propose a new implementation of the alternating-fixpoint method in which false atoms are computed in a top-down fashion. We show that our algorithm is faster than other known algorithms and that for a wide class of programs it is linear and so, asymptotically optimal.

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 programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.

Characterizations of semi-stable and stage extensions in terms of two-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming counterparts of the notion of range which is an established concept in argumentation semantics.

The W3C Web Ontology Language (OWL) is a powerful knowledge representation formalism at the basis of many semantic-centric applications. Since its unrestricted usage makes reasoning undecidable already in case of very simple tasks, expressive yet decidable fragments have been identified. Among them, we focus on OWL 2 RL, which offers a rich variety of semantic constructors, apart from supporting all RDFS datatypes. Although popular Web resources - such as DBpedia - fall in OWL 2 RL, only a few systems have been designed and implemented for this fragment. None of them, however, fully satisfy all the following desiderata: (i) being freely available and regularly maintained; (ii) supporting query answering and SPARQL queries; (iii) properly applying the sameAs property without adopting the unique name assumption; (iv) dealing with concrete datatypes. To fill the gap, we present DaRLing, a freely available Datalog rewriter for OWL 2 RL ontological reasoning under SPARQL queries. In particular, we describe its architecture, the rewriting strategies it implements, and the result of an experimental evaluation that demonstrates its practical applicability.

In this note, we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of Temporal Equilibrium Logic that shares the syntax of first-order Linear-time Temporal Logic but has different semantics, selecting some Linear-time Temporal Logic models we call temporal stable models. Then, we consider a subclass of theories (called splittable temporal logic programs) that are close to usual logic programs but allowing a restricted use of temporal operators. In this setting, we provide a syntactic definition of safe variables that suffices to show the property of domain independence – that is, addition of arbitrary elements in the universe does not vary the set of temporal stable models. Finally, we present a method for computing the derivable facts by constructing a non-temporal logic program with variables that is fed to a standard Answer Set Programming grounder. The information provided by the grounder is then used to generate a subset of ground temporal rules which is equivalent to (and generally smaller than) the full program instantiation.