Temporal theories of reasoning

Abstract

In this paper we describe a general way of formalizing reasoning behaviour. Such a behaviour may be described by all the patterns which are valid for the behaviour. A pattern can be seen as a sequence of information states which describe what has been derived at each time point. A transition from an information state at a point in time to the state at the (or a) next time point is induced by one or more inference steps. We choose to model the information states by partial models and the patterns either by linear time or branching time temporal models. Using temporal logic one can define theories and look at all models of that theory. For a number of examples of reasoning behaviour we have been able to definetemporal theories such that its (minimal) models correspond to the valid patterns of the behaviour. These theories prescribe that the inference steps which are possible, are "executed" in the temporal model. The examples indicate that partial temporal logic is a powerful means of describing and formalizing complex reasoning patterns, as the dynamic aspects of reasoning systems are integrated into the static ones in a clear fashion.

Redesign and reuse in compositional knowledge-based systems

“…In this paper, informal descriptions of these concepts are presented. The formal semantics of design processes (based on partial logic for the states and temporal partial logic [15] for the reasoning traces (sequences of states)) are discussed by Brazier, Langen, and Treur [3]. design object description is a conservative modification of the first, • design object description modification steps: a relation which holds between two design object descriptions if the second design object description is a modification of the first (allowing revision, for example).…”

A Logical Theory of Design

“…Partial models are a means to formalise information states, representing incomplete world descriptions (e.g., Langen and Treur, 1989); types of world descriptions relevant for design are design object descriptions and requirement sets. To obtain formal semantics of reasoning behaviour in design tasks, a recently developed approach based on partial temporal models is adopted, which has shown to be applicable to different types of (non-monotonic) reasoning (see Engelfriet and Treur, 1994;Gavrila and Treur, 1994;Treur, 1994). Semantics of a reasoning process is formalised by a set of (alternative) reasoning traces, represented by a partial temporal model, i.e., a sequence of partial models.…”

Model-Based Default Refinement of Partial Information within an Ambient Agent

“…The general idea underlying the approach followed here, and inspired by [8,9], is that a particular reasoning line can be formalised by a sequence of information states M 0 , M 1 , ...... . Here any M t is a description of the (partial) information that has been derived up to time point t. From a dynamic perspective, an inference step, performed in time duration D is viewed as a transition M t → → → → M t+D of a current information state M t to a next information state M t+D .…”

“…[8,9]. In practical reasoning situations usually different lines of reasoning can be generated, each leading to a distinct set of conclusions.…”

“…The method exploits the available causal model and allows the use of software tools to determine the different default extensions that form the possible interpretations, given the sensor information and the causal model. Moreover, by formally specifying the default rules in an executable temporal format, according to the approach put forward in [8,9], explicit default reasoning processes can be generated. Section 2 describes two case studies used to illustrate the approach.…”