44 research outputs found
Formal verification of a generic framework to synthesize SAT-provers
We present in this paper an application of the ACL2 system to generate
and reason about propositional satis ability provers. For that purpose, we develop a
framework where we de ne a generic SAT-prover based on transformation rules, and
we formalize this generic framework in the ACL2 logic, carrying out a formal proof of
its termination, soundness and completeness. This generic framework can be
instantiated to obtain a number of veri ed and executable SAT-provers in ACL2, and
this can be done in an automated way. Three instantiations of the generic framework
are considered: semantic tableaux, sequent and Davis-Putnam-Logeman-Loveland
methods.Ministerio de Ciencia y TecnologÃa TIC2000-1368-C03-0
Verification in ACL2 of a Generic Framework to Synthesize SAT–Provers
We present in this paper an application of the ACL2 system
to reason about propositional satisfiability provers. For that purpose,
we present a framework where we define a generic transformation based
SAT–prover, and we show how this generic framework can be formalized
in the ACL2 logic, making a formal proof of its termination, soundness
and completeness. This generic framework can be instantiated to obtain
a number of verified and executable SAT–provers in ACL2, and this
can be done in an automatized way. Three case studies are considered:
semantic tableaux, sequent and Davis–Putnam methods.Ministerio de Ciencia y TecnologÃa TIC2000-1368-C03-0
Formal Verification of Molecular Computational Models in ACL2: A Case Study
Theorem proving is a classical AI problem with a broad range
of applications. Since its complexity is exponential in the size of the
problem, many methods to parallelize the process has been proposed.
One of these approaches is based on the massive parallelism of molecular
reactions. ACL2 is an automated theorem prover especially adequate for
algorithm verification. In this paper we present an ACL2 formalization
of a molecular computational model: Adleman’s restricted model. As
an application of this model, an implementation of Lipton’s experiment
solving SAT is described. We use ACL2 to make a formal proof of the
completeness and soundness properties of this implementation.Ministerio de Ciencia y TecnologÃa TIC2000-1368-C03-0
Proof Pearl: a Formal Proof of Higman’s Lemma in ACL2
Higman’s lemma is an important result in infinitary combinatorics, which
has been formalized in several theorem provers. In this paper we present a formalization
and proof of Higman’s Lemma in the ACL2 theorem prover. Our formalization
is based on a proof by Murthy and Russell, where the key termination argument
is justified by the multiset relation induced by a well-founded relation. To our
knowledge, this is the first mechanization of this proof.Ministerio de Ciencia e Innovación MTM2009-13842-C02-0
Formal Correctness of a Quadratic Unification Algorithm
We present a case study using ACL2 [5] to verify a non-trivial algorithm
that uses efficient data structures. The algorithm receives as input two first-order
terms and it returns a most general unifier of these terms if they are unifiable, failure
otherwise. The verified implementation stores terms as directed acyclic graphs by
means of a pointer structure. Its time complexity is O(n2) and its space complexity
is O(n), and it can be executed in ACL2 at a speed comparable to a similar C
implementation. We report the main issues encountered to achieve this formally
verified implementation
Constructing Formally Verified Reasoners for the ALC Description Logic
Description Logics are a family of logics used to represent and reason about conceptual and terminological
knowledge. Recently, its importance has been increased since they are used as a basis for the Ontology
Web Language (OWL) used for the Semantic Web. In previous work, we have developed in PVS a generic
framework for reasoning in the ALC description logic, proving its termination, soundness and completeness.
In this paper we present the construction, from the generic framework, of a formally verified generic tableau–
based algorithm for checking satisfiability of ALC –concepts. We do it using a methodology of refinements
to transfer the properties from the framework to the algorithm. We also obtain some verified reasoners from
the algorithm by a process of instantiation.Ministerio de Educación y Ciencia TIN2004–0388
Formal proofs about rewriting using ACL2
We present an application of the ACL2 theorem prover to reason about rewrite systems
theory. We describe the formalization and representation aspects of our work using the firstorder,
quantifier-free logic of ACL2 and we sketch some of the main points of the proof effort.
First, we present a formalization of abstract reduction systems and then we show how this
abstraction can be instantiated to establish results about term rewriting. The main theorems
we mechanically proved are Newman’s lemma (for abstract reductions) and Knuth–Bendix
critical pair theorem (for term rewriting).Ministerio de Educación y Ciencia TIC2000-1368-CO3-0
A Theory About First-Order Terms in ACL2
We describe the development in ACL2 of a library of results about first-order
terms. In particular, we present the formalization of some of the main properties of the
complete lattice of first-order terms with respect to the subsumption relation. As a byproduct,
verified executable implementations are obtained for some basic operations on firstorder
terms, including matching, renaming, unification and anti-unification. This work can
be seen as a basis for further studies about the formal properties of automated reasoning
and symbolic computation systems.Ministerio de Ciencia y TecnologÃa TIC2000-1368-CO3-0
Extending Attribute Exploration by Means of Boolean Derivatives
We present a translation of problems of Formal Context
Analysis into ideals problems in F2[x] through the Boolean derivatives.
The Boolean derivatives are introduced as a kind of operators on propositional
formulas which provide a complete calculus. They are useful to
refine stem basis as well as for extending attribute exploration
A logic-algebraic tool for reasoning with Knowledge-Based Systems
A detailed exposition of foundations of a logic-algebraic model for reasoning
with knowledge bases speci ed by propositional (Boolean) logic is presented.
The model is conceived from the logical translation of usual derivatives on
polynomials (on residue rings) which is used to design a new inference rule of
algebro-geometric inspiration. Soundness and (refutational) completeness of
the rule are proved. Some applications of the tools introduced in the paper
are shown.Ministerio de EconomÃa y Competitividad TIN2013-41086-