10th International Conference on
Artificial Intelligence and Symbolic Computation
AISC 2010
Paris, France, 5th6th July 2010
Accepted Papers
The list of accepted papers below is ordered alphabetically
by first author surname.
Links to preprints (on http://ArXiv.org) and to the final
published articles (on http://www.springerlink.com) will be
added as they become available.
 Iterms in ordered resolution and superposition calculi : retrieving lost completeness
Hicham Bensaid, Ricardo Caferra and Nicolas Peltier
Abstract:
Ordered resolution and superposition are the stateoftheart
proof procedures used in saturationbased theorem proving, for non equational and equational clause se
ts respectively.
In
this paper, we present extensions of these calculi that permit one to
reason about formulae built from terms
with integer exponents (or Iterms), a schematisation language
allowing one to denote infinite sequences of iterated terms.
We prove that the ordered resolution calculus is still refutationally complete
when applied on (non equational) clauses containing Iterms.
In the equational case, we prove that the superposition
calculus is not complete in the presence of Iterms and we devise a new inference
rule, called Hsuperposition, that restores completeness.
[Preprint] [SpringerLink]
 Structured Formal Development with Quotient Types in Isabelle/HOL
Maksym Bortin and Christoph Lüth
Abstract:
General purpose theorem provers provide sophisticated proof
methods, but lack some of the advanced structuring mechanisms found
in specification languages. This paper builds on previous work extending
the theorem prover Isabelle with such mechanisms. A way to build the
quotient type over a given base type and an equivalence relation on it,
and a generalised notion of folding over quotiented types is given as a
formalised highlevel step called a design tactic. The core of this paper
are four axiomatic theories capturing the design tactic. The applicability
is demonstrated by derivations of implementations for finite multisets
and finite sets from lists in Isabelle. [Preprint] [SpringerLink]
 Instantiation of SMT problems modulo Integers
Mnacho Echenim and Nicolas Peltier
Abstract:
Many decision procedures for SMT problems rely more or
less implicitly on an instantiation of the axioms defining the theories
under consideration, and differ by making use of the additional properties
of each theory, in order to increase efficiency. We present a new technique
for devising complete instantiation schemes on SMT problems over a
combination of linear arithmetic with another theory
T . The method
consists in first instantiating the arithmetic part of the formula, and
then getting rid of the remaining variables in the problem by using an
instantiation strategy which is complete for
T . We provide examples
evidencing that not only is this technique generic (in the sense that it
applies to a wide range of theories) but it is also efficient, even compared
to stateoftheart instantiation schemes for specific theories. [Preprint] [SpringerLink]
 On Krawtchouk Transforms
Philip Feinsilver and Rene Schott
Abstract:
Krawtchouk polynomials appear in a variety of contexts,
most notably as orthogonal polynomials and in coding theory via the
Krawtchouk transform. We present an operator calculus formulation of
the Krawtchouk transform that is suitable for computer implementation.
A positivity result for the Krawtchouk transform is shown. Then our approach is compared with the use of the Krawtchouk transform in coding
theory where it appears in MacWilliams' and Delsarte's theorems on
weight enumerators. [Preprint] [SpringerLink]
 A mathematical model of the competition between acquired immunity and virus
Mikhail Kolev
Abstract:
A mathematical model describing the interactions between
viral infection and acquired immunity is proposed. The model is formulated in terms of a system of partial integrodifferential bilinear equations. Results of numerical experiments are presented.
[Preprint] [SpringerLink]
 Some Notes upon "When does <T> equal sat(T)?"
Yongbin Li
Abstract:
Given a regular set T in K[x], Lemaire et al. in ISSAC'08 give
a nice algebraic property: the regular set T generates its saturated ideal
if and only if it is primitive. We dirstly aim at giving a more direct proof
of the above result, generalizing the concept of primitivity of polynomials
and regular sets and presenting a new result which is equivalent to the
above property. On the other hand, based upon correcting an error of
the definition of Uset in AISC'06, we further develop some geometric
properties of triangular sets. To a certain extent, the relation between
the primitivity of T and its Uset is also revealed in this paper.
[Preprint] [SpringerLink]
 How to correctly prune tropical trees
JeanVincent Loddo and Luca Saiu
Abstract:
We present _tropical games_, a generalization of combinatorial minmax games
based on tropical algebras. Our model breaks the traditional symmetry of
rational zerosum games where players have exactly opposed goals (min vs.
max), is more widely applicable than minmax and also supports a form of
pruning, despite it being less effective than alphabeta. Actually, minmax
games may be seen as particular cases where both the game and its dual are
tropical: when the dual of a tropical game is also tropical, the power of
alphabeta is completely recovered. We formally develop the model and prove
that the tropical pruning strategy is correct, then conclude by showing how
the problem of approximated parsing can be modeled as a tropical game,
profiting from pruning. [Preprint] [SpringerLink]
 From matrix interpretations over the rationals to matrix interpretations over the naturals
Salvador Lucas
Abstract:
Matrix interpretations generalize linear polynomial interpretations and have been proved useful in the implementation of tools for
automatically proving termination of Term Rewriting Systems. In view
of the successful use of rational coefficients in polynomial interpretations, we have recently generalized traditional matrix interpretations (using natural numbers in the matrix entries) to incorporate real numbers.
However, existing results which formally prove that polynomials over the
reals are more powerful than polynomials over the naturals for proving
termination of rewrite systems failed to be extended to matrix interpretations. In this paper we get deeper into this problem. We show that,
under some conditions, it is possible to transform a matrix interpretation
over the rationals satisfying a set of symbolic constraints into a matrix
interpretation over the naturals (using bigger matrices) which still satisfies the constraints.
[Preprint] [SpringerLink]
 Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
Josef Urban and Geoff Sutcliffe
Abstract:
This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called
MizAR, similar to the SystemOnTPTP service for firstorder automated
reasoning. The main differences to SystemOnTPTP are the use of the
Mizar language that is oriented towards human mathematicians (rather
than the pure firstorder logic used in SystemOnTPTP), and setting the
service in the context of the large Mizar Mathematical Library of previous theorems, definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new
challenges and new opportunities for automated reasoning and for proof
presentation tools. This paper describes the overall structure of MizAR,
and presents the automated reasoning systems and proof presentation
tools that are combined to make MizAR a useful mathematical service. [Preprint] [SpringerLink]
