Hypothetical-reasoning and radical non-constituent coordination in categorical logic

The paper investigates the connection between non-constituent coordination, as implemented in categorial grammar by means of a polymorphic type-assignment to lexical conjunctions, and hypothetical reasoning in Categorial Logics. A way of extending the logic is suggested, so that coordination can be applied to types depending on undischarged assumptions. By a certain ``resource manipulation'' of assumptions (of hypothetical reasoning), a late-discharge is facilitated, leading to what is referred to as the {em radical non-constituent coordination, wherby only basic types (and not functional types of any kind) are coordinated

Probably Safe or Live

This paper presents a formal characterisation of safety and liveness properties \`a la Alpern and Schneider for fully probabilistic systems. As for the classical setting, it is established that any (probabilistic tree) property is equivalent to a conjunction of a safety and liveness property. A simple algorithm is provided to obtain such property decomposition for flat probabilistic CTL (PCTL). A safe fragment of PCTL is identified that provides a sound and complete characterisation of safety properties. For liveness properties, we provide two PCTL fragments, a sound and a complete one. We show that safety properties only have finite counterexamples, whereas liveness properties have none. We compare our characterisation for qualitative properties with the one for branching time properties by Manolios and Trefler, and present sound and complete PCTL fragments for characterising the notions of strong safety and absolute liveness coined by Sistla

Personal note: Working with Farhad Arbab 1990–2005

From 1990 to 2005 the author had the privilege and pleasure to work as a programmer in Farhad Arbab’s research group, initially on the development, implementation and applications of the Manifold coordination language