From Linear to Branching-Time Temporal Logics: Transfer of Semantics and Definability

This 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 tree

A probabilistic extension of UML statecharts: specification and verification

This paper is the extended technical report that corresponds to a published paper [14]. This paper introduces means to specify system randomness within UML statecharts, and to verify probabilistic temporal properties over such enhanced statecharts which we call probabilistic UML statecharts. To achieve this, we develop a general recipe to extend a statechart semantics with discrete probability distributions, resulting in Markov decision processes as semantic models. We apply this recipe to the requirements-level UML semantics of [8]. Properties of interest for probabilistic statecharts are expressed in PCTL, a probabilistic variant of CTL for processes that exhibit both non-determinism and probabilities. Verification is performed using the model checker Prism. A model checking example shows the feasibility of the suggested approach

Logical operators for ontological modeling

We show that logic has more to offer to ontologists than standard first order and modal operators. We first describe some operators of linear logic which we believe are particularly suitable for ontological modeling, and suggest how to interpret them within an ontological framework. After showing how they can coexist with those of classical logic, we analyze three notions of artifact from the literature to conclude that these linear operators allow for reducing the ontological commitment needed for their formalization, and even simplify their logical formulation

Studies on modal logics of time and space

This dissertation presents original results in Temporal Logic and Spatial Logic. Part I concerns Branching-Time Logic. Since Prior 1967, two main semantics for Branching-Time Logic have been devised: Peircean and Ockhamist semantics. Zanardo 1998 proposed a general semantics, called Indistinguishability semantics, of which Peircean and Ockhamist semantics are limit cases. We provide a finite axiomatization of the Indistinguishability logic of upward endless bundled trees using a non-standard inference rule, and prove that this logic is strongly complete. In Part II, we study the temporal logic given by the tense operators F for future and P for past together with the derivative operator , interpreted on the real numbers. We prove that this logic is neither strongly nor Kripke complete, it is PSPACE-complete, and it is finitely axiomatizable. In Part III, we study the spatial logic given by the derivative operator and the graded modalities {n | n in N}. We prove that this language, call it L, is as expressive as the first-order language Lt of Flum and Ziegler 1980 when interpreted on T3 topological spaces. Then, we give a general definition of modal operator: essentially, a modal operator will be defined by a formula of Lt with at most one free variable. If a modal operator is defined by a formula predicating only over points, then it is called point-sort operator. We prove that L, even if enriched with all point-sort operators, however enriched with finitely many modal operators predicating also on open sets, cannot express Lt on T2 spaces. Finally, we axiomatize the logic of any class between all T1 and all T3 spaces and prove that it is PSPACE-complete.Open Acces