27 research outputs found
Compilability of Abduction
Abduction is one of the most important forms of reasoning; it has been
successfully applied to several practical problems such as diagnosis. In this
paper we investigate whether the computational complexity of abduction can be
reduced by an appropriate use of preprocessing. This is motivated by the fact
that part of the data of the problem (namely, the set of all possible
assumptions and the theory relating assumptions and manifestations) are often
known before the rest of the problem. In this paper, we show some complexity
results about abduction when compilation is allowed
Automated Synthesis of Tableau Calculi
This paper presents a method for synthesising sound and complete tableau
calculi. Given a specification of the formal semantics of a logic, the method
generates a set of tableau inference rules that can then be used to reason
within the logic. The method guarantees that the generated rules form a
calculus which is sound and constructively complete. If the logic can be shown
to admit finite filtration with respect to a well-defined first-order semantics
then adding a general blocking mechanism provides a terminating tableau
calculus. The process of generating tableau rules can be completely automated
and produces, together with the blocking mechanism, an automated procedure for
generating tableau decision procedures. For illustration we show the
workability of the approach for a description logic with transitive roles and
propositional intuitionistic logic.Comment: 32 page
Using Linear Temporal Logic to Model and Solve Planning Problems
In this work we investigate the use of propositional linear temporal logic LTL as a specification language for planning problems and the use of analytic tableaux as a tool for plan search, following the “planning as satisfiability” approach [11]. We claim that LTL can be a good specification language for planning problems, because of its rich expressive power and the underlying simple model of time and actions. We propose the use of Tabplan, a tableau calculus for bounded model search in LTL (fully described in [7]), as a system for plan synthesis. We show how to code a given planning problem by means of different LTL theories, each encoding making the model construction procedure simulate a different search strategy, namely planning by progression and partial order regression planning in the style of [14]
An efficient approach to nominal equalities in hybrid logic tableaux
Basic hybrid logic extends modal logic with the possibility of naming worlds by means of a distinguished class of atoms (called nominals) and the so-called
satisfaction operator, that allows one to state that a given formula holds at the world named a, for some nominal a.
Hence, in particular, hybrid formulae include ``equality'' assertions,
stating that two nominals are distinct names for the same world.
The treatment of such nominal equalities in proof systems for
hybrid logics
may induce many redundancies.
This paper introduces an internalized tableau system for basic
hybrid logic, significantly reducing such redundancies.
The calculus enjoys a
strong termination property: tableau
construction terminates without relying on
any specific rule application strategy, and
no loop-checking is needed.
The treatment of nominal
equalities specific of the proposed calculus is briefly compared to
other approaches. Its practical advantages are demonstrated by
empirical results obtained by use of implemented systems.
Finally, it is briefly shown how to extend the calculus to include the global and converse modalities