223 research outputs found
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
Dual Forgetting Operators in the Context of Weakest Sufficient and Strongest Necessary Conditions
Forgetting is an important concept in knowledge representation and automated
reasoning with widespread applications across a number of disciplines. A
standard forgetting operator, characterized in [Lin and Reiter'94] in terms of
model-theoretic semantics and primarily focusing on the propositional case,
opened up a new research subarea. In this paper, a new operator called weak
forgetting, dual to standard forgetting, is introduced and both together are
shown to offer a new more uniform perspective on forgetting operators in
general. Both the weak and standard forgetting operators are characterized in
terms of entailment and inference, rather than a model theoretic semantics.
This naturally leads to a useful algorithmic perspective based on quantifier
elimination and the use of Ackermman's Lemma and its fixpoint generalization.
The strong formal relationship between standard forgetting and strongest
necessary conditions and weak forgetting and weakest sufficient conditions is
also characterized quite naturally through the entailment-based, inferential
perspective used. The framework used to characterize the dual forgetting
operators is also generalized to the first-order case and includes useful
algorithms for computing first-order forgetting operators in special cases.
Practical examples are also included to show the importance of both weak and
standard forgetting in modeling and representation
Ilinva: Using Abduction to Generate Loop Invariants
International audienceWe describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize in-ductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large set of programming languages and application domains; and lazy, in the sense that it only generates invariants that allow one to derive the required properties. It relies on an existing system called GPiD for abductive reasoning modulo theories [14], and on the platform for program verification Why3 [16]. Experiments show evidence of the practical relevance of our approach
The PIE Environment for First-Order-Based Proving, Interpolating and Eliminating
Abstract The PIE system aims at providing an environment for creating complex applications of automated first-order theorem proving techniques. It is embedded in Prolog. Beyond actual proving tasks, also interpolation and second-order quantifier elimination are supported. A macro feature and a L A T E X formula pretty-printer facilitate the construction of elaborate formalizations from small, understandable and documented units. For use with interpolation and elimination, preprocessing operations allow to preserve the semantics of chosen predicates. The system comes with a built-in default prover that can compute interpolants
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