Formal verification of a proof procedure for the description logic ALC

PorJosé A. Alonso

Se ha publicado un artñiculo de razonamiento formalizado en Isabelle/HOL titulado Formal verification of a proof procedure for the description logic ALC.

Sus autores son

  • Mohamed Chaabani (LIMOSE, Universidad de Boumerdes, Argelia),
  • Mohamed Mezghiche (LIMOSE, Universidad de Boumerdes, Argelia) y
  • Martin Strecker (IRIT (Institut de Recherche en Informatique de Toulouse), Francia)

El trabajo se presentó en el SCSS 2012 (Fourth International Symposium on
Symbolic Computation in Software Science), cuyas actas se publicaron la semana pasada.

Su resumen es

Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER and FaCT++, have been implemented, but these provers themselves have not been yet certified. In order to ensure the soundness of derivations in these DLs, it is necessary to formally verify the deductions applied by these reasoners. Formal methods offer powerful tools for the specification and verification of proof procedures, among them there are methods for proving properties such as soundness, completeness and termination of a proof procedure. In this paper, we present the definition of a proof procedure for the Description Logic ALC, based on a semantic tableau method. We ensure validity of our prover by proving its soundness, completeness and termination properties using Isabelle proof assistant. The proof proceeds in two phases, first by establishing these properties on an abstract level, and then by instantiating them for an implementation based on lists.

En el 2007 presentamos una formalización análoga en PVS: A formally verified prover for the ALC description logic.

Exámenes de programación funcional con Haskell

PorJosé A. Alonso

He publicado el libro Exámenes de programación funcional con Haskell (2009-2013) en el que recopilo los exámenes de la asignatura de Informática (de primero del Grado en Matemáticas) desde el curso 2009-10 hasta el actual. El libro contiene 74 exámenes y 475 ejercicios.

Este libro es el complemento de los anteriores:

Pratt’s primality certificates

PorJosé A. Alonso

Se ha publicado un artículo de razonamiento formalizado en Isabelle/HOL titulado Pratt’s primality certificates.

Su autores son Simon Wimmer y Lars Noschinski (Technische Universität München).

El artículo se ha publicado el 22 de julio en el Archive of Formal Proofs.

Su resumen es

In 1975, Pratt introduced a proof system for certifying primes. He showed that a number p is prime iff a primality certificate for p exists. By showing a logarithmic upper bound on the length of the certificates in size of the prime number, he concluded that the decision problem for prime numbers is in NP. This work formalizes soundness and completeness of Pratt’s proof system as well as an upper bound for the size of the certificate.

Reasoning about higher-order relational specifications

PorJosé A. Alonso

Se ha publicado un artículo de razonamiento formalizado en Abella titulado Reasoning about higher-order relational specifications.

Sus autores son

El trabajo se presentará en septiembre en el PPDP 2013 (15th International Symposium on Principles and Practice of Declarative Programming).

Su resumen es

The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to encoding side conditions and contexts that occur frequently in structural operational semantics (SOS) style presentations. Specifications are often useful in reasoning about the systems they describe. The Abella theorem prover supports such reasoning by explicitly embedding the specification logic within a rich reasoning logic; specifications are then reasoned about through this embedding. However, realizing an induction principle in the face of dynamically changing assumption sets is nontrivial and the original Abella system uses only a subset of the HH specification logic for this reason. We develop a method here for supporting inductive reasoning over all of HH. Our approach takes advantage of a focusing property of HH to isolate the use of an assumption and the ability to finitely characterize the structure of any such assumption in the reasoning logic. We demonstrate the effectiveness of these ideas via several specification and meta-theoretic reasoning examples that have been implemented in an extended version of Abella.