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Publication# On Satisfiability for Quantified Formulas in Instantiation-Based Procedures

Abstract

Procedures for first-order logic with equality are used in many modern theorem provers and solvers, yet procedure termination in case of interesting sub-classes of satisfiable formulas remains a challenging problem. We present an instantiation-based semi-decision procedure defined on a fragment of many-sorted first-order logic that succeeds on certain satisfiable formulas even if they contain, for example, associativity axioms. The models for which our procedure terminates have finite ranges of function symbols. We expect that our procedure can be integrated into other instantiating procedures such as E-matching with little performance impact. Our procedure is also compatible with specialized verification techniques that enable efficient reasoning about pure higher-order recursive functions. We integrated our procedure into the Leon verification framework. The implementation is publicly available and has been evaluated on non-trivial benchmarks featuring higher-order programs with quantified contracts.

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Related concepts (33)

Related publications (35)

Related MOOCs (3)

Ontological neighbourhood

First-order logic

First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable.

Second-order logic

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle).

Higher-order logic

In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic. The term "higher-order logic" is commonly used to mean higher-order simple predicate logic.

Parallel programming

With every smartphone and computer now boasting multiple processors, the use of functional ideas to facilitate parallel programming is becoming increasingly widespread. In this course, you'll learn th

Parallel programming

With every smartphone and computer now boasting multiple processors, the use of functional ideas to facilitate parallel programming is becoming increasingly widespread. In this course, you'll learn th

Parallel programming

With every smartphone and computer now boasting multiple processors, the use of functional ideas to facilitate parallel programming is becoming increasingly widespread. In this course, you'll learn th

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We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having po ...
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Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and fun ...

2023We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of the accepted word ...

2023