57 research outputs found
QCDCL vs QBF Resolution: Further Insights
We continue the investigation on the relations of QCDCL and QBF resolution systems. In particular, we introduce QCDCL versions that tightly characterise QU-Resolution and (a slight variant of) long-distance Q-Resolution. We show that most QCDCL variants - parameterised by different policies for decisions, unit propagations and reductions - lead to incomparable systems for almost all choices of these policies
The Logic of Partitions: Introduction to the Dual of the Logic of Subsets
Modern categorical logic as well as the Kripke and topological models of
intuitionistic logic suggest that the interpretation of ordinary
"propositional" logic should in general be the logic of subsets of a given
universe set. Partitions on a set are dual to subsets of a set in the sense of
the category-theoretic duality of epimorphisms and monomorphisms--which is
reflected in the duality between quotient objects and subobjects throughout
algebra. If "propositional" logic is thus seen as the logic of subsets of a
universe set, then the question naturally arises of a dual logic of partitions
on a universe set. This paper is an introduction to that logic of partitions
dual to classical subset logic. The paper goes from basic concepts up through
the correctness and completeness theorems for a tableau system of partition
logic
Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics
Belief revision of knowledge bases represented by a set of sentences in a
given logic has been extensively studied but for specific logics, mainly
propositional, and also recently Horn and description logics. Here, we propose
to generalize this operation from a model-theoretic point of view, by defining
revision in an abstract model theory known under the name of satisfaction
systems. In this framework, we generalize to any satisfaction systems the
characterization of the well known AGM postulates given by Katsuno and
Mendelzon for propositional logic in terms of minimal change among
interpretations. Moreover, we study how to define revision, satisfying the AGM
postulates, from relaxation notions that have been first introduced in
description logics to define dissimilarity measures between concepts, and the
consequence of which is to relax the set of models of the old belief until it
becomes consistent with the new pieces of knowledge. We show how the proposed
general framework can be instantiated in different logics such as
propositional, first-order, description and Horn logics. In particular for
description logics, we introduce several concrete relaxation operators tailored
for the description logic \ALC{} and its fragments \EL{} and \ELext{},
discuss their properties and provide some illustrative examples
Computing explanations for interactive constraint-based systems
Constraint programming has emerged as a successful paradigm for modelling
combinatorial problems arising from practical situations. In many of those situations,
we are not provided with an immutable set of constraints. Instead, a user
will modify his requirements, in an interactive fashion, until he is satisfied with
a solution. Examples of such applications include, amongst others, model-based
diagnosis, expert systems, product configurators.
The system he interacts with must be able to assist him by showing the consequences
of his requirements. Explanations are the ideal tool for providing this
assistance. However, existing notions of explanations fail to provide sufficient information.
We define new forms of explanations that aim to be more informative.
Even if explanation generation is a very hard task, in the applications we consider,
we must manage to provide a satisfactory level of interactivity and, therefore, we
cannot afford long computational times.
We introduce the concept of representative sets of relaxations, a compact set of
relaxations that shows the user at least one way to satisfy each of his requirements
and at least one way to relax them, and present an algorithm that efficiently computes
such sets. We introduce the concept of most soluble relaxations, maximising
the number of products they allow. We present algorithms to compute such relaxations
in times compatible with interactivity, achieving this by indifferently making
use of different types of compiled representations. We propose to generalise
the concept of prime implicates to constraint problems with the concept of domain
consequences, and suggest to generate them as a compilation strategy. This sets a
new approach in compilation, and allows to address explanation-related queries in
an efficient way. We define ordered automata to compactly represent large sets of
domain consequences, in an orthogonal way from existing compilation techniques
that represent large sets of solutions
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