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Satisfiability Modulo Theories (SMT) specifications often rely on quantifiers to remain concise and declarative. However, checking the satisfiability of such specifications directly can be inefficient. A common optimization is to ground the…
Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory…
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…
We define the concept of a monotonic theory and show how to build efficient SMT (SAT Modulo Theory) solvers, including effective theory propagation and clause learning, for such theories. We present examples showing that monotonic theories…
We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of…
We present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model…
We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently…
We present our extension of ACL2 with Satisfiability Modulo Theories (SMT) solvers using ACL2's trusted clause processor mechanism. We are particularly interested in the verification of physical systems including Analog and Mixed-Signal…
Dependent types offer great versatility and power, but developing proofs with them can be tedious and requires considerable human guidance. We propose to integrate Satisfiability Modulo Theories (SMT)-based refinement types into the…
We introduce an approach that aims to combine the usage of satisfiability modulo theories (SMT) solvers with the Combinatory Logic Synthesizer (CL)S framework. (CL)S is a tool for the automatic composition of software components from a…
Traditional Answer Set Programming (ASP) rests upon one-shot solving. A logic program is fed into an ASP system and its stable models are computed. The high practical relevance of dynamic applications led to the development of multi-shot…
Answer set programming (ASP) is an efficient problem-solving approach, which has been strongly supported both scientifically and technologically by several solvers, ongoing active research, and implementations in many different fields.…
Answer Set Programming (ASP) is a well-known problem-solving formalism in computational logic. Nowadays, ASP is used in many real world scenarios thanks to ASP solvers. Standard evaluation of ASP programs suffers from an intrinsic…
The SMT (Satisfiability Modulo Theories) theory of arrays is well-established and widely used, with variousdecision procedures and extensions developed for it. However, recent works suggest that developing tailoredreasoning for some…
We propose an end-to-end approach for Answer Set Programming (ASP) and linear algebraically compute stable models satisfying given constraints. The idea is to implement Lin-Zhao's theorem together with constraints directly in vector spaces…
LPMLN is a recent addition to probabilistic logic programming languages. Its main idea is to overcome the rigid nature of the stable model semantics by assigning a weight to each rule in a way similar to Markov Logic is defined. We present…
Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new…
Answer Set Programming (ASP) is a powerful declarative programming paradigm commonly used for solving challenging search and optimization problems. The modeling languages of ASP are supported by sophisticated solving algorithms (solvers)…
The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications.…