90 research outputs found
Timelines Are Expressive Enough to Capture Action-Based Temporal Planning
Planning problems are usually expressed by specifying which actions can be
performed to obtain a given goal. In temporal planning problems, actions come
with a time duration and can overlap in time, which noticeably increase the
complexity of the reasoning process. Action-based temporal planning has been
thoroughly studied from the complexity-theoretic point of view, and has been
proved to be EXPSPACE-complete in its general formulation. Conversely,
timeline-based planning problems are represented as a collection of variables
whose time-varying behavior is governed by a set of temporal constraints, called
synchronization rules. Timelines provide a unified framework to reason about
planning and execution under uncertainty. Timeline-based systems are being
successfully employed in real-world complex tasks, but, in contrast to
action-based planning, little is known on their computational complexity and
expressiveness. In particular, a comparison of the expressiveness of the action-
and timeline-based formalisms is still missing. This paper contributes a first
step in this direction by proving the EXPSPACE-completeness of timeline-based
planning with no temporal horizon and bounded temporal relations only. The
result is shown via a reduction from action-based temporal planning, thus
proving that timelines are expressive enough to capture it
A Game-Theoretic Approach to Timeline-Based Planning with Uncertainty
In timeline-based planning, domains are described as sets of independent, but interacting, components, whose behaviour over time (the set of timelines) is governed by a set of temporal constraints. A distinguishing feature of timeline-based planning systems is the ability to integrate planning with execution by synthesising control strategies for flexible plans. However, flexible plans can only represent temporal uncertainty, while more complex forms of nondeterminism are needed to deal with a wider range of realistic problems. In this paper, we propose a novel game-theoretic approach to timeline-based planning problems, generalising the state of the art while uniformly handling temporal uncertainty and nondeterminism. We define a general concept of timeline-based game and we show that the notion of winning strategy for these games is strictly more general than that of control strategy for dynamically controllable flexible plans. Moreover, we show that the problem of establishing the existence of such winning strategies is decidable using a doubly exponential amount of space
A framework for modelling Molecular Interaction Maps
Metabolic networks, formed by a series of metabolic pathways, are made of
intracellular and extracellular reactions that determine the biochemical
properties of a cell, and by a set of interactions that guide and regulate the
activity of these reactions. Most of these pathways are formed by an intricate
and complex network of chain reactions, and can be represented in a human
readable form using graphs which describe the cell cycle checkpoint pathways.
This paper proposes a method to represent Molecular Interaction Maps
(graphical representations of complex metabolic networks) in Linear Temporal
Logic. The logical representation of such networks allows one to reason about
them, in order to check, for instance, whether a graph satisfies a given
property , as well as to find out which initial conditons would guarantee
, or else how can the the graph be updated in order to satisfy .
Both the translation and resolution methods have been implemented in a tool
capable of addressing such questions thanks to a reduction to propositional
logic which allows exploiting classical SAT solvers.Comment: 31 pages, 12 figure
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
On the Complexity of Finding Second-Best Abductive Explanations
While looking for abductive explanations of a given set of manifestations, an
ordering between possible solutions is often assumed. The complexity of
finding/verifying optimal solutions is already known. In this paper we consider
the computational complexity of finding second-best solutions. We consider
different orderings, and consider also different possible definitions of what a
second-best solution is
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
A Prover Dealing with Nominals, Binders, Transitivity and Relation Hierarchies
This work describes the Sibyl prover, an implementation of a tableau based proof procedure for multi-modal hybrid logic with the converse, graded and global modalities, and enriched with features largely used in description logics: transitivity and relation hierarchies. The proof procedure is provably terminating when the input problem belongs to an expressive decidable fragment of hybrid logic. After a description of the implemented proof procedure, the way how the implementation deals with the most delicate aspects of the calculus is explained. Some experimental results, run on sets of randomly generated problems as well as some hand-tailored ones, show only a moderate deterioration in the performances of the prover when the number of transitivity and inclusion axioms increase. Sibyl is compared with other provers (HTab, the hybrid logic prover whose expressive power is closer to Sibyl's one, and the first-order prover SPASS). The obtained results show that Sibyl has reasonable performances
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