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Abstract Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence (AI) has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling search-optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements. Recall integer linear programming, MaxSAT, optimization satisfiability modulo theory, (constraint) answer set programming. These paradigms vary significantly in their languages in ways they express quality conditions on computed solutions. Here we propose a unifying framework of so-called extended weight systems that eliminates syntactic distinctions between paradigms. They allow us to see essential similarities and differences between optimization statements provided by distinct automated reasoning languages. We also study formal properties of the proposed systems that immediately translate into formal properties of paradigms that can be captured within our framework. 

This paper studies the problem of arguing program correctness for logic programs with aggregates in the context of Answer Set Programming. Cabalar, Fandinno, and Lierler (2020) championed a modular methodology for arguing program correctness. We show how a recently proposed many-sorted semantics for logic programs with aggregates allows us to apply their methodology to this type of program. This is illustrated using well-known encodings for the Graph Coloring and Traveling Salesman problems. In particular, we showcase how this modular approach allows us to reuse the proof of correctness of a Hamiltonian Cycle encoding studied in a previous publication when considering the Traveling Salesman program. 

Conditional literals are an expressive Answer Set Programming language construct supported by the solver clingo. Their semantics are currently defined by a translation to infinitary propositional logic, however, we develop an alternative characterization with the SM operator which does not rely on grounding. This allows us to reason about the behavior of a broad class of clingo programs/encodings containing conditional literals, without referring to a particular input/instance of an encoding. We formalize the intuition that conditional literals behave as nested implications, and prove the equivalence of our semantics to those implemented by clingo. 

Answer set programming (ASP) has long been used for modeling and solving hard search problems. Experience shows that the performance of ASP tools on different ASP encodings of the same problem may vary greatly from instance to instance and it is rarely the case that one encoding outperforms all others. We describe a system and its implementation that given a set of encodings and a training set of instances, builds performance models for the encodings, predicts the execution time of these encodings on new instances, and uses these predictions to select an encoding for solving. 

The paper presents a characterization of logic programs with aggregates based on many-sorted generalization of operator SM that refers neither to grounding nor to fixpoints. This characterization introduces new symbols for aggregate operations and aggregate elements, whose meaning is fixed by adding appropriate axioms to the result of the SM transformation. We prove that for programs without positive recursion through aggregates our semantics coincides with the semantics of the answer set solver Clingo. 

Abstract Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially different answer set programs exist for a given problem. Sometimes these encodings may display significantly different performance. Uncovering precise formal links between these programs is often important and yet far from trivial. This paper presents formal results carefully relating a number of interesting program rewritings. It also provides the proof of correctness of system projector concerned with automatic program rewritings for the sake of efficiency. 

Abstract Constraint answer set programming or CASP, for short, is a hybrid approach in automated reasoning putting together the advances of distinct research areas such as answer set programming, constraint processing, and satisfiability modulo theories. CASP demonstrates promising results, including the development of a multitude of solvers: acsolver, clingcon, ezcsp, idp, inca, dingo, mingo, aspmt2smt, clingo[l,dl], and ezsmt . It opens new horizons for declarative programming applications such as solving complex train scheduling problems. Systems designed to find solutions to constraint answer set programs can be grouped according to their construction into, what we call, integrational or translational approaches. The focus of this paper is an overview of the key ingredients of the design of constraint answer set solvers drawing distinctions and parallels between integrational and translational approaches. The paper also provides a glimpse at the kind of programs its users develop by utilizing a CASP encoding of Traveling Salesman problem for illustration. In addition, we place the CASP technology on the map among its automated reasoning peers as well as discuss future possibilities for the development of CASP.