6 research outputs found
Instantiation of SMT problems modulo Integers
Many decision procedures for SMT problems rely more or less implicitly on an
instantiation of the axioms of the theories under consideration, and differ by
making use of the additional properties of each theory, in order to increase
efficiency. We present a new technique for devising complete instantiation
schemes on SMT problems over a combination of linear arithmetic with another
theory T. The method consists in first instantiating the arithmetic part of the
formula, and then getting rid of the remaining variables in the problem by
using an instantiation strategy which is complete for T. We provide examples
evidencing that not only is this technique generic (in the sense that it
applies to a wide range of theories) but it is also efficient, even compared to
state-of-the-art instantiation schemes for specific theories.Comment: Research report, long version of our AISC 2010 pape
The Model Evolution Calculus with Equality
In many theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the Model Evolution calculus (ME), a first-order version of the propositional DPLL procedure. The new calculus, MEE, is a proper extension of the ME calculus without equality. Like ME it maintains an explicit ``candidate model'', which is searched for by DPLL-style splitting. For equational reasoning MEE uses an adapted version of the ordered paramodulation inference rule, where equations used for paramodulation are drawn (only) from the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many simplification techniques known from superposition-style theorem proving. Our main result is the refutational completeness of the MEE calculus
Integration of equational reasoning into instantiation-based theorem proving
In this paper we present a method for integrating equational reasoning into instantiation-based theorem proving. The method employs a satisfiability solver for ground equational clauses together with an instance generation process based on an ordered paramodulation type calculus for literals. The completeness of the procedure is proved using the the model generation technique, which allows us to justify redundancy elimination based on appropriate orderings
Integration of equational reasoning into instantiation-based theorem proving
In this paper we present a method for integrating equational reasoning into
instantiation-based theorem proving. The method employs a satisfiability solver
for ground equational clauses together with an instance generation process
based on an ordered paramodulation type calculus for literals. The completeness
of the procedure is proved using the the model generation technique, which
allows us to justify redundancy elimination based on appropriate orderings
Integration of equational reasoning into instantiation-based theorem proving
In this paper we present a method for integrating equational reasoning into
instantiation-based theorem proving. The method employs a satisfiability solver
for ground equational clauses together with an instance generation process
based on an ordered paramodulation type calculus for literals. The completeness
of the procedure is proved using the the model generation technique, which
allows us to justify redundancy elimination based on appropriate orderings