3,301 research outputs found
Decidability of the interval temporal logic ABBar over the natural numbers
In this paper, we focus our attention on the interval temporal logic of the
Allen's relations "meets", "begins", and "begun by" (ABBar for short),
interpreted over natural numbers. We first introduce the logic and we show that
it is expressive enough to model distinctive interval properties,such as
accomplishment conditions, to capture basic modalities of point-based temporal
logic, such as the until operator, and to encode relevant metric constraints.
Then, we prove that the satisfiability problem for ABBar over natural numbers
is decidable by providing a small model theorem based on an original
contraction method. Finally, we prove the EXPSPACE-completeness of the proble
On Relaxing Metric Information in Linear Temporal Logic
Metric LTL formulas rely on the next operator to encode time distances,
whereas qualitative LTL formulas use only the until operator. This paper shows
how to transform any metric LTL formula M into a qualitative formula Q, such
that Q is satisfiable if and only if M is satisfiable over words with
variability bounded with respect to the largest distances used in M (i.e.,
occurrences of next), but the size of Q is independent of such distances.
Besides the theoretical interest, this result can help simplify the
verification of systems with time-granularity heterogeneity, where large
distances are required to express the coarse-grain dynamics in terms of
fine-grain time units.Comment: Minor change
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
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