1,721,018 research outputs found
A Road Map of Interval Temporal Logics and Duration Calculi
Full text linkWe survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature
and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results
From linear to branching-time temporal logics: transfer of semantics and definability
Full text linkThis paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees
Interval Temporal Logics:A Journey
No full textWe discuss a family of modal logics for reasoning about relational structures of intervals over (usually) linear orders, with modal operators associated with the various binary relations between such intervals, known as Allen’s interval relations. The formulae of these logics are evaluated at intervals rather than points and the main eect of that semantic feature is substantially higher expressiveness and computational complexity of the interval logics as compared to point-based ones. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in it over the past 10 years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of interval logics
Expressiveness of the Interval Logics of Allen's Relations on the Class of all Linear Orders: Complete Classification
No full textWe compare the expressiveness of the fragments of Halpern and Shoham’s interval logic (HS), i.e., of all interval logics with modal operators associated with Allen’s relations between intervals in linear orders. We establish a complete set of interdefinability equations between these modal operators, and thus obtain a complete classification of the family of 212 fragments of HS with respect to their expressiveness. Using that result and a computer program, we have found that there are 1347 expressively different such interval logics over the class of all linear orders
The dark side of Interval Temporal Logics: sharpening the undecidability border
No full textUnlike the Moon, the dark side of interval temporal logics is the one we usually see: their ubiquitous undecidability. Identifying minimal undecidable interval logics is thus a natural and important issue in the research agenda in the area. The decidability status of a logic often depends on the class of models (in our case, the class of interval structures) in which it is interpreted. In this paper, we have identified several new minimal undecidable logics amongst the fragments of Halpern-Shoham logic HS, including the logic of the overlaps relation, over the classes of all and finite linear orders, as well as the logic of the meet and subinterval relations, over the class of dense linear orders. Together with previous undecidability results, this work contributes to delineate the border of the dark side of interval temporal logics quite sharply
A General Tableau Method for Propositional Interval Temporal Logics
No full textLogics for time intervals provide a natural framework for
representing and reasoning about timing properties in various areas of
computer science. However, while various tableau methods have been de-
veloped for linear and branching time point-based temporal logics, not
much work has been done on tableau methods for interval-based temporal
logics. In this paper, we introduce a new, very expressive propositional
interval temporal logic, called (Non-Strict) Branching CDT (BCDT+)
which extends most of the propositional interval temporal logics pro-
posed in the literature. Then, we provide BCDT+ with a generic tableau
method which combines features of explicit tableau methods for modal
logics with constraint label management and the classical tableau method
for ̄rst-order logic, and we prove its soundness and completeness
A simple semantics for Aristotelian apodeictic syllogistics
No full textWe give a simple definition of validity for syllogisms involving necessary and assertoric premises which validates all and only the Aristotelian apodeictic syllogisms
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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