Tense and the Logic of Change

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Towards a general temporal theory

The research work presented herein addresses time representation and temporal reasoning in the domain of artificial intelligence. A general temporal theory, as an extension of Alien and Hayes', Gallon's and Vilain's theories, is proposed which treats both time intervals and time points on an equal footing; that is, both intervals and points are taken as primitive time elements in the theory. This means that neither do intervals have to be constructed out of points, nor do points have to be created as some limiting construction of intervals. This approach is different from that of Ladkin, of Van Beek, of Dechter, Meiri and Pearl, and of Maiocchi, which is either to construct intervals out of points, or to treat points and intervals separately. The theory is presented in terms of a series of axioms which characterise a single temporal relation, "meets", over time elements. The axiomatisation allows non-linear time structures such as branching time and parallel time, and additional axioms specifying the linearity and density of time are specially presented. A formal characterisation for the open and closed nature of primitive intervals, which has been a problematic question of time representation in artificial intelligence, is provided in terms of the "meets" relation. It is shown to be consistent with the conventional definitions of open/closed intervals which are constructed out of points. It is also shown that this general theory is powerful enough to subsume some representative temporal theories, such as Alien and Hayes's interval based theory, Bruce's and McDermott's point based theories, and the interval and point based theory of Vilain, and of Gallon. A finite time network based on the theory is specially addressed, where a consistency checker in two different forms is provided for cases with, and without, duration reasoning, respectively. Utilising the time axiomatisation, the syntax and semantics of a temporal logic for reasoning about propositions whose truth values are associated with particular intervals/points are explicitly defined. It is shown that the logic is more expressive than that of some existing systems, such as Alien's interval-based logic, the revised theory proposed by Gallon, Shoham's point-based interval logic, and Haugh's MTA based logic; and the corresponding problems with these systems are satisfactorily solved. Finally, as an application of the temporal theory, a new architecture for a temporal database system which allows the expression of relative temporal knowledge of data transaction and data validity times is proposed. A general retrieval mechanism is presented for a database with a purely qualitative temporal component which allows queries with temporal constraints in terms of any logical combination of Alien's temporal relations. To reduce the computational complexity of the consistency checking algorithm when quantitative time duration knowledge is added, a class of databases, termed time-limited databases, is introduced. This class allows absolute-time-stamped and relative time information in a form which is suitable for many practical applications, where qualitative temporal information is only occasionally needed, and the efficient retrieval mechanisms for absolute-time-stamped databases may be adopted

Modelling causal reasoning

PhDAlthough human causal reasoning is widely acknowledged as an object of scientific enquiry, there is little consensus on an appropriate measure of progress. Up-to-date evidence of the standard method of research in the field shows that this method has been rejected at the birth of modern science. We describe an instance of the standard scientific method for modelling causal reasoning (causal calculators). The method allows for uniform proofs of three relevant computational properties: correctness of the model with respect to the intended model, full abstraction of the model (function) with respect to the equivalence of reasoning scenarios (input), and formal relations of equivalence and subsumption between models. The method extends and exploits the systematic paradigm [Handbook of Logic in Artificial Intelligence and Logic Programming, volume IV, p. 439-498, Oxford 1995] to fit with our interpretation of it. Using the described method, we present results for some major models, with an updated summary spanning seventy-two years of research in the field

Detecting bots with temporal logic

Social bots are computer programs that act like human users on social media platforms. Social bot detection is a rapidly growing field dominated by machine learning approaches. In this paper, we propose a complementary method to machine learning by exploring bot detection as a model checking problem. We introduce Temporal Network Logic (TNL) which we use to specify social networks where agents can post and follow each other. Using this logic, we formalize different types of social bot behavior with formulas that are satisfied in a model of a network with bots. We also consider an extension of the logic where we explore the expressive power of including elements from hybrid logic in our framework. We give model checking algorithms for TNL and its hybrid extension, and show that the complexity of the former is in P and the latter in PSPACE.publishedVersio