2,299 research outputs found
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order
logic modulo background theories, in particular some form of integer
arithmetic. A major unsolved research challenge is to design theorem provers
that are "reasonably complete" even in the presence of free function symbols
ranging into a background theory sort. The hierarchic superposition calculus of
Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we
demonstrate, not optimally. This paper aims to rectify the situation by
introducing a novel form of clause abstraction, a core component in the
hierarchic superposition calculus for transforming clauses into a form needed
for internal operation. We argue for the benefits of the resulting calculus and
provide two new completeness results: one for the fragment where all
background-sorted terms are ground and another one for a special case of linear
(integer or rational) arithmetic as a background theory
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory
More SPASS with Isabelle: superposition with hard sorts and configurable simplification
Sledgehammer for Isabelle/HOL integrates automatic theorem provers to discharge interactive proof obligations. This paper considers a tighter integration of the superposition prover SPASS to increase Sledgehammer’s success rate. The main enhancements are native support for hard sorts (simple types) in SPASS, simplification that honors the orientation of Isabelle simp rules, and a pair of clause-selection strategies targeted at large lemma libraries. The usefulness of this integration is confirmed by an evaluation on a vast benchmark suite and by a
case study featuring a formalization of language-based security
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
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