On Gabbay's temporal fixed point operator

AbstractWe discuss the temporal logic “USF”, involving Until, Since and the fixed point operator ϑ of Gabbay, with semantics over the natural numbers. We show that any formula not involving Until is equivalent to one without nested fixed point operators. We then prove that USF has expressive power matching that of the monadic second-order logic S1S. The proof shows that any USF-formula is equivalent to one with at most two nested fixed point operators — i.e., no branch of its formation tree has more than two ϑ's. We then axiomatise USF and prove that it is decidable, with PSPACE-complete satisfiability problem. Finally, we discuss an application of these results to the executable temporal logic system “MetateM”

Hierarchies of modal and temporal logics with reference pointers

. We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: "point of reference --- reference pointer" which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. The universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and strong completeness theorem is proved for them and extended to some classes of their extensions. Key words: Modal and Temporal Logics, Reference Pointers, Expressi..

Time granularity in simulation models within a multi-agent system

The understanding of how processes in natural phenomena interact at different scales of time has been a great challenge for humans. How information is transferred across scales is fundamental if one tries to scale up from finer to coarse levels of granularity. Computer simulation has been a powerful tool to determine the appropriate amount of detail one has to impose when developing simulation models of such phenomena. However, it has proved difficult to represent change at many scales of time and subject to cyclical processes. This issue has received little attention in traditional AI work on temporal reasoning but it becomes important in more complex domains, such as ecological modelling. Traditionally, models of ecosystems have been developed using imperative languages. Very few of those temporal logic theories have been used for the specification of simulation models in ecology. The aggregation of processes working at different scales of time is difficult (sometimes impossible) to do reliably. The reason is because these processes influence each other, and their functionality does not always scale to other levels. Thus the problems to tackle are representing cyclical and interacting processes at many scales and providing a framework to make the integration of such processes more reliable. We propose a framework for temporal modelling which allows modellers to represent cyclical and interacting processes at many scales. This theory combines both aspects by means of modular temporal classes and an underlying special temporal unification algorithm. To allow integration of different models they are developed as agents with a degree of autonomy in a multi-agent system architecture. This Ecoagency framework is evaluated on ecological modelling problems and it is compared to a formal language for describing ecological systems

CLiFF Notes: Research in the Language Information and Computation Laboratory of The University of Pennsylvania

This report takes its name from the Computational Linguistics Feedback Forum (CLIFF), an informal discussion group for students and faculty. However the scope of the research covered in this report is broader than the title might suggest; this is the yearly report of the LINC Lab, the Language, Information and Computation Laboratory of the University of Pennsylvania. It may at first be hard to see the threads that bind together the work presented here, work by faculty, graduate students and postdocs in the Computer Science, Psychology, and Linguistics Departments, and the Institute for Research in Cognitive Science. It includes prototypical Natural Language fields such as: Combinatorial Categorial Grammars, Tree Adjoining Grammars, syntactic parsing and the syntax-semantics interface; but it extends to statistical methods, plan inference, instruction understanding, intonation, causal reasoning, free word order languages, geometric reasoning, medical informatics, connectionism, and language acquisition. With 48 individual contributors and six projects represented, this is the largest LINC Lab collection to date, and the most diverse