1,757 research outputs found
Deduction modulo theory
This paper is a survey on Deduction modulo theor
New results on rewrite-based satisfiability procedures
Program analysis and verification require decision procedures to reason on
theories of data structures. Many problems can be reduced to the satisfiability
of sets of ground literals in theory T. If a sound and complete inference
system for first-order logic is guaranteed to terminate on T-satisfiability
problems, any theorem-proving strategy with that system and a fair search plan
is a T-satisfiability procedure. We prove termination of a rewrite-based
first-order engine on the theories of records, integer offsets, integer offsets
modulo and lists. We give a modularity theorem stating sufficient conditions
for termination on a combinations of theories, given termination on each. The
above theories, as well as others, satisfy these conditions. We introduce
several sets of benchmarks on these theories and their combinations, including
both parametric synthetic benchmarks to test scalability, and real-world
problems to test performances on huge sets of literals. We compare the
rewrite-based theorem prover E with the validity checkers CVC and CVC Lite.
Contrary to the folklore that a general-purpose prover cannot compete with
reasoners with built-in theories, the experiments are overall favorable to the
theorem prover, showing that not only the rewriting approach is elegant and
conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page
Automated theorem proving in first-order logic modulo: on the difference between type theory and set theory
Resolution modulo is a first-order theorem proving method that can be applied
both to first-order presentations of simple type theory (also called
higher-order logic) and to set theory. When it is applied to some first-order
presentations of type theory, it simulates exactly higherorder resolution. In
this note, we compare how it behaves on type theory and on set theory
Logic Programming as Constructivism
The features of logic programming that
seem unconventional from the viewpoint of classical logic
can be explained in terms of constructivistic logic. We
motivate and propose a constructivistic proof theory of
non-Horn logic programming. Then, we apply this formalization
for establishing results of practical interest.
First, we show that 'stratification can be motivated in a
simple and intuitive way. Relying on similar motivations,
we introduce the larger classes of 'loosely stratified' and
'constructively consistent' programs. Second, we give a
formal basis for introducing quantifiers into queries and
logic programs by defining 'constructively domain
independent* formulas. Third, we extend the Generalized
Magic Sets procedure to loosely stratified and constructively
consistent programs, by relying on a 'conditional
fixpoini procedure
Constructions of free commutative integro-differential algebras
In this survey, we outline two recent constructions of free commutative
integro-differential algebras. They are based on the construction of free
commutative Rota-Baxter algebras by mixable shuffles. The first is by
evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004
Set of support, demodulation, paramodulation: a historical perspective
This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field
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