Reasoning about perception of depth and about spatial relations between moving physical objects is a challenging problem. We investigate the representation of depth and motion by means of depth profiles whereby each object in the world is represented as a single peak. We propose a logical theory, formulated in the situation calculus (SC), that is used for reasoning about object motion (includin...

The topic of this panel is whether considerations of logicality or rationality should be paramount in modelling, or reasoning about, knowledge and belief. The first reaction one ought to have to such a question is to ask why there should be any conflict between these two types of consideration. Isn't one required to be logical in order to be rational? On closer examination, the issue is not as ...

Feature structures are informational elements that have been used in several linguistic theories and in computational systems for natural language processing. A logical calculus has been developed and used as a description language for feature structures. In the present work, a framework in three-valued logic is suggested for defining the semantics of a feature structure description language, a...

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values...

We present a logical calculus which imposes a grading on a sequent-style calculus to account for the runtime of the programmes represented by the sequents. This system is sound for a notion of polynomial-time realizability. An extension of the grading is also considered, giving a notion of \dependant grades", which is also sound. Furthermore, we deene a notion of closed graded multicategory, an...