We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory (...) subsuming mereology. Some more speculative strategies and directions for further research are also considered. (shrink)

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

/ Part INTRODUCTION Fuzziness is not a priori an obvious concept and demands some explanation. "Fuzziness" is what Black (NF) calls "vagueness" when ...

Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate high-level qualitative spatial information in a flexible way would be extremely useful. Such capabilities can be proveded by logical calculi; and indeed 1st-order theories of certain spatial relations have been given [20]. But computing inferences in 1st-order logic is generally intractable unless special (...) methods are known.0-order modal logics provide an alternative representation which is more expressive than classical 0-order logic and yet often more amenable to automated deduction than 1st-order formalisms. These calculi are usually interpreted as propositional logics: non-logical constants are taken as denoting propositions. However, they can also be given a nominal interpretation in which the constants stand for some kind of object. I show how 0-order logics can be given a spatial interpretation: constants denote regions and logical operators correspond to operations on regions which are important for characterising spatial situations.Representing certain spatial concepts requires the introduction of modal operators, interpreted as functions generating regions related in specific ways to those denoted by their arguments. A significant example is the convex-hull operator whose value is the smallest convex region containing its argument. I investigate how this this operator can be captured in a multi-medal logic. (shrink)

A person's cognitive map, or knowledge of large‐scale space, is built up from observations gathered as he travels through the environment. It acts as a problem solver to find routes and relative positions, as well as describing the current location. The TOUR model captures the multiple representations that make up the cognitive map, the problem‐solving strategies it uses, and the mechanisms for assimilating new information. The representations have rich collections of states of partial knowledge, which support many of the performance (...) characteristics of common‐sense knowledge. (shrink)

This second volume in the Counterpoints Series focuses on alternative models of visual-spatial processing in human cognition. The editors provide a historical and theoretical introduction and offer ideas about directions and new research designs.