Satisfiability Modulo Theories and Assignments

Bonacina, Maria Paola; Graham-Lengrand, Stéphane; Shankar, Natarajan

doi:10.1007/978-3-319-63046-5_4

Cited by 18 publications

(31 citation statements)

References 14 publications

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“…Other approaches lift the CDCL procedure to the Bernays-Schönfinkel fragment, which allows only formulae of the form ∃ * ∀ * ϕ, where ϕ contains neither quantifiers nor occurrences of function symbols [50,1]. Section 3.2 returns to SMT with a summary of an inference system named CDSAT, that generalizes MCSAT to generic combinations of theories [10,11]. Section 3.3 discusses how the SMT problem itself can be generalized to the SMA problem, for satisfiability modulo assignments.…”

Section: General Conflict-driven Methodsmentioning

confidence: 99%

“…. , T n [10,11]. This extension is crucial for the development of the conflict-driven paradigm, because problems from applications seldom involve only one theory.…”

Section: A Taste Of the Cdsat Frameworkmentioning

confidence: 99%

“…Initial assignments are justified assignments with empty justification. Other justified assignments are due to the conflict-solving rules of the CDSAT inference system [10,11].…”

Section: A Taste Of the Cdsat Frameworkmentioning

confidence: 99%

“…Therefore, it is precisely the abstraction of combining inference systems rather than procedures that allows CDSAT to handle both conflict-driven and black-box T k -satisfiability procedures, thereby generalizing not only MCSAT, but also equality sharing. Theory modules for propositional logic, and the quantifier-free fragments of the theory of equality, linear rational arithmetic, and the theory of arrays with extensionality are provided as examples [10,11].…”

Section: A Taste Of the Cdsat Frameworkmentioning

confidence: 99%

“…The strategy is deemed conflict-driven, if it uses inferences to explain and solve the conflict repairing the model. This paper offers in Section 2 a necessarily incomplete overview of the state of the art in conflict-driven methods, while Section 3 advertises two recent conflict-driven methods: Semantically-Guided Goal-Sensitive reasoning (SGGS), for full first-order logic [16,17,18], and Conflict-Driven Satisfiability (CDSAT), for satisfiability modulo a generic combination of theories, and for a new class of problems called satisfiability modulo assignments (SMA) [10,11].…”

Section: Introductionmentioning

confidence: 99%

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On Conflict-Driven Reasoning

Bonacina

Kalpa Publications in Computing

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Automated formal methods and automated reasoning are interconnected, as formal methods generate reasoning problems and incorporate reasoning techniques. For example, formal methods tools employ reasoning engines to find solutions of sets of constraints, or proofs of conjectures. From a reasoning perspective, the expressivity of the logical language is often directly proportional to the difficulty of the problem. In propositional logic, Conflict-Driven Clause Learning (CDCL) is one of the key features of state-of-the-art satisfiability solvers. The idea is to restrict inferences to those needed to explain conflicts, and use conflicts to prune a backtracking search. A current research direction in automated reasoning is to generalize this notion of conflict-driven satisfiability to a paradigm of conflict-driven reasoning in first-order theories for satisfiability modulo theories and assignments, and even in full first-order logic for generic automated theorem proving. While this is a promising and exciting lead, it also poses formidable challenges.

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Section: General Conflict-driven Methodsmentioning

confidence: 99%

“…. , T n [10,11]. This extension is crucial for the development of the conflict-driven paradigm, because problems from applications seldom involve only one theory.…”

Section: A Taste Of the Cdsat Frameworkmentioning

confidence: 99%

“…Initial assignments are justified assignments with empty justification. Other justified assignments are due to the conflict-solving rules of the CDSAT inference system [10,11].…”

Section: A Taste Of the Cdsat Frameworkmentioning

confidence: 99%

Section: A Taste Of the Cdsat Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Conflict-Driven Reasoning

Bonacina

Kalpa Publications in Computing

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Theory Combination: Beyond Equality Sharing

Bonacina

Fontaine

Ringeissen

et al. 2019

Lecture Notes in Computer Science

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Satisfiability is the problem of deciding whether a formula has a model. Although it is not even semidecidable in first-order logic, it is decidable in some first-order theories or fragments thereof (e.g., the quantifier-free fragment). Satisfiability modulo a theory is the problem of determining whether a quantifier-free formula admits a model that is a model of a given theory. If the formula mixes theories, the considered theory is their union, and combination of theories is the problem of combining decision procedures for the individual theories to get one for their union. A standard solution is the equality-sharing method by Nelson and Oppen, which requires the theories to be disjoint and stably infinite. This paper surveys selected approaches to the problem of reasoning in the union of disjoint theories, that aim at going beyond equality sharing, including: asymmetric extensions of equality sharing, where some theories are unrestricted, while others must satisfy stronger requirements than stable infiniteness; superposition-based decision procedures; and current work on conflict-driven satisfiability (CDSAT).

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