And-or tableaux for fixpoint logics with converse: LTL, CTL, PDL and CPDL

Over the last forty years, computer scientists have invented or borrowed numerous logics for reasoning about digital systems. Here, I would like to concentrate on three of them: Linear Time Temporal Logic (LTL), branching time Computation Tree temporal Logic (CTL), and Propositional Dynamic Logic (PDL), with and without converse. More specifically, I would like to present results and techniques on how to solve the satisfiability problem in these logics, with global assumptions, using the tableau method. The issues that arise are the typical tensions between computational complexity, practicality and scalability. This is joint work with Linh Anh Nguyen, Pietro Abate, Linda Postniece, Florian Widmann and Jimmy Thomson

An On-the-fly Tableau-based Decision Procedure for PDL-Satisfiability

We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from bad loops during backtracking. It is easy to implement, with potential for parallelisation, because it constructs a pseudo-model ``on the fly'' by exploring each tableau branch independently. But its worst-case behaviour is 2EXPTIME rather than EXPTIME. A prototype implementation in the TWB (http://twb.rsise.anu.edu.au) is available.Comment: 26 pages, longer version of article in Methods for Modalities 2007; improved readability of proof

Relations between Propositional Normal Modal Logics: an Overview

The modal logic literature is notorious for multiple axiomatizations of the same logic and for conflicting overloading of axiom names. Many of the interesting interderivability results are still scattered over the often hard to obtain classics. We catalogue the most interesting axioms, their numerous variants, and explore the relationships between them in terms of interderivability as both axiom (schema) and as simple formulae. In doing so we introduce the Logics Workbench (LWB, see http://lwbwww.uniba.ch:8080/LWBinfo.html), a versatile tool for proving theorems in numerous propositional (nonclassical) logics. As a side-effect we fulfill a call from the modal theorem proving community for a database of known theorem

Effects of the numbers of foliar insecticide applications on the production of the oilseed watermelon citrullus lanatus

Citrullus lanatus is a creeping annual vine species belong to Cucurbitaceae. This plant is cultivated for its oleaginous seeds that are important in the social and cultural life of several peoples in Africa. Thus to improve its production field studies were conducted during two cropping seasons of 2007 to define an economically beneficial foliar insecticide application frequency to manage insect pests on the oleaginous C. lanatus in a woodland savannah zone of Côte d’Ivoire. Zero (control) to four sprays of a foliar carbamate-based insecticide (Cypercal EC 50) were  applied at four plant growth stages (seedling emergence, stem creeping, male flowering, and female flowering) in a completely randomised block design experiment. Four beetles and one ladybird species were identified as the most damaging insect pests on the target crop. Seed yield and most of the yield components analyzed increased with increasing number of sprays, the highest values being obtained with 3-4 sprays, according to the growing season. Between seasons variations were noted for the seed yield and all the yield components, and attributed to the negative influence of low temperature and heavy rainfalls occurring during the second growing season (18 July to 16 December 2007).Keywords. Foliar insecticide, Carbamate, Citrullus lanatus, Cucurbitaceae, Yield, pest insects, beetles, ladybird

Le géosymbole, vecteur de la territorialité régionale. L’exemple du fest-noz en Bretagne

Cet article vise à mettre en relation la notion de territorialité régionale et le concept de géosymbole. Développé par Joël Bonnemaison pour expliquer la relation symbolique entre la société mélanésienne et son territoire, le concept de géosymbole est repris dans cet article pour analyser le rapport collectif que la société bretonne contemporaine entretient avec le sien. La société bretonne contemporaine produit des formes spatiales qui ont une dimension identitaire. La majorité de ces marqueurs spatiaux sont d’origine paysagère. Mais en dehors de la matérialité des paysages, il existe, à travers la pratique du fest-noz, des formes spatiales vectrices de la territorialité bretonne. Principal espace d’expression pour la musique bretonne, le fest-noz contribue au renouvellement du patrimoine vivant – musique et danse – de la région. C’est un symbole moderne de l’attachement des Bretons à leur territoire. Il participe à la construction symbolique du territoire régional.This paper aims at establishing a relationship between the notion of regional territoriality and the concept of geosymbol. Developed by Bonnemaison (Bonnemaison, 1994) this concept tries to explain the symbolic link between melanesian society and its territory. This paper re-uses this concept to analyse the collective relationship between the breton contemporary society and its territory. The breton contemporary society produces various spatial forms who have a “identity” dimension. The majority of these spatial markers derive from elements of landscape. But beside the landscapes’ materiality, through the practice of fest-noz, an other type of cultural place appears, that enhance breton identity. As a major place for expression of breton music, fest-noz provides the revival of regional living heritage – music and dance. It is a modern symbol of breton’s attachment for territory. It takes part in symbolic construction of the regional territory

Reasoning about obligations in Obligationes : a formal approach.

Despite the appearance of `obligation' in their name, medieval obligational dispu- tations between an Opponent and a Respondent seem to many to be unrelated to deontic logic. However, given that some of the example disputations found in me- dieval texts involve Respondent reasoning about his obligations within the context of the disputation, it is clear that some sort of deontic reasoning is involved. In this paper, we explain how the reasoning diers from that in ordinary basic deontic logic, and dene dynamic epistemic semantics within which the medieval obligations can be expressed and the examples evaluated. Obligations in this framework are history- based and closely connected to action, thus allowing for comparisons with, e.g., the knowledge-based obligations of Pacuit, Parikh, and Cogan, and stit-theory. The con- tributions of this paper are twofold: The introduction of a new type of obligation into the deontic logic family, and an explanation of the precise deontic concepts involved in obligationes