A Proposal for Reasoning in Agents: Restricted Entailment

Abstract

Johnson-Laird proposes a semantic theory of human reasoning taking into account finite human capacities. We cast this into logical formalism and define a notion of restricted semantic entailment. Corresponding to any set of logical structures, R, there is a restricted entailment with parameter R. The family of restricted entailments, generated as R varies over sets of structures, is shown to be a complete lattice and to approximate ordinary entailment in the sense of domain theory. A given restricted entailment, $\vDash_{R}$ say, can be modelled in a modal language with an operator ↓ _R . The modal language is sound and complete and there is a correspondence result: $X\vDash_{R} \varphi$ iff $\downarrow\!\!_{R} X \Vdash \downarrow\!\!_{R}\varphi$, where X is a set of first-order sentences and ϕ is first-order. This forms the basis for the proposal that $\vDash_{R}$ be identified with agent reasoning and that ↓ _R encapsulate an agent. The existence of the lattice structure mentioned above means that several agents can be integrated into a super-agent or else distilled into a sub-agent by taking joins or meets.