3,194 research outputs found
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
Efficient Encodings of First-Order Horn Formulas in Equational Logic
We present several translations from first-order Horn formulas to equational logic. The goal of these translations is to allow equational theorem provers to efficiently reason about non-equational problems. Using these translations we were able to solve 37 problems of rating 1.0 (i.e. which had not previously been automatically solved) from the TPTP
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
Tractable approximate deduction for OWL
Acknowledgements This work has been partially supported by the European project Marrying Ontologies and Software Technologies (EU ICT2008-216691), the European project Knowledge Driven Data Exploitation (EU FP7/IAPP2011-286348), the UK EPSRC project WhatIf (EP/J014354/1). The authors thank Prof. Ian Horrocks and Dr. Giorgos Stoilos for their helpful discussion on role subsumptions. The authors thank Rafael S. Gonçalves et al. for providing their hotspots ontologies. The authors also thank BoC-group for providing their ADOxx Metamodelling ontologies.Peer reviewedPostprin
Hypertableau Reasoning for Description Logics
We present a novel reasoning calculus for the description logic SHOIQ^+---a
knowledge representation formalism with applications in areas such as the
Semantic Web. Unnecessary nondeterminism and the construction of large models
are two primary sources of inefficiency in the tableau-based reasoning calculi
used in state-of-the-art reasoners. In order to reduce nondeterminism, we base
our calculus on hypertableau and hyperresolution calculi, which we extend with
a blocking condition to ensure termination. In order to reduce the size of the
constructed models, we introduce anywhere pairwise blocking. We also present an
improved nominal introduction rule that ensures termination in the presence of
nominals, inverse roles, and number restrictions---a combination of DL
constructs that has proven notoriously difficult to handle. Our implementation
shows significant performance improvements over state-of-the-art reasoners on
several well-known ontologies
Twee: An Equational Theorem Prover
Twee is an automated theorem prover for equational logic. It implements unfailing Knuth-Bendix completion with ground joinability testing and a connectedness-based redundancy criterion. It came second in the UEQ division of CASC-J10, solving some problems that no other system solved. This paper describes Tweeâs design and implementation
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
Perspectives in deductive databases
AbstractI discuss my experiences, some of the work that I have done, and related work that influenced me, concerning deductive databases, over the last 30 years. I divide this time period into three roughly equal parts: 1957â1968, 1969â1978, 1979âpresent. For the first I describe how my interest started in deductive databases in 1957, at a time when the field of databases did not even exist. I describe work in the beginning years, leading to the start of deductive databases about 1968 with the work of Cordell Green and Bertram Raphael. The second period saw a great deal of work in theorem providing as well as the introduction of logic programming. The existence and importance of deductive databases as a formal and viable discipline received its impetus at a workshop held in Toulouse, France, in 1977, which culminated in the book Logic and Data Bases. The relationship of deductive databases and logic programming was recognized at that time. During the third period we have seen formal theories of databases come about as an outgrowth of that work, and the recognition that artificial intelligence and deductive databases are closely related, at least through the so-called expert database systems. I expect that the relationships between techniques from formal logic, databases, logic programming, and artificial intelligence will continue to be explored and the field of deductive databases will become a more prominent area of computer science in coming years
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