Frame-Structure Logic with Extended Attribute Relations

Abstract

Most logical approaches to knowledge representation and reasoning are based on predicate logic. In predicate logic, a proposition is constructed from predicates, functions, individual variables and quantifiers. Although predicate logic is highly expressive, the structure of the formulas that are produced is different to that of natural language. This difference is a result of the constructors that are used, particularly individual variables. In an effort to rectify this situation, the authors have proposed Frame-Structure Logic (FSL), in which propositions have a structure that resembles that of natural language. In FSL, objects that correspond to a noun phrase are constructed from basic objects and attribute pairs. For example, “students who like certain fruits” is described in FSL by “student [Favorite → {fruit}]”. In predicate logic, the same object is described by “λx∃y(student(x) ∧ Favorite(x, y) ∧ fruit(y))”. Certainly, the structure of modification in natural language can be explicitly reflected in FSL. In this paper, in order to enrich the expressive power of basic FSL, new attribute relations are proposed. And an axiomatic system of extended logic is constructed as FSL For example, “students who like all kinds of fruits” is described by “student [Favorite ← {fruit}]”, and the following relations holds. student [Favorite ← {fruit}] $\vDash$ student [Favorite → {fruit}]

Furthermore, an attribute function is introduced into FS1. For example, “objects that are kept as pets by students” is described as “Pet(student)” and a compound notion “black dogs that are kept as pets by students” can be constructed using an object operator “·” as “Pet(student). dog [Color→ black]”. The notation of Frame-Structure Logic is based on that of F-logic and Quixote. In contrast to these similar logic systems, FS1 has the following features.

• 1. There are no individual variables in logical formulas

• 2. Attribute relations can be treated as objects

• 3. FS1 has mathematical semantics that are different from that in predicate logic and an axiomatic system complete under the semantics

Knowledge representation that is similar to the structure of natural language is possible as a result of Feature 1. Feature 2 allows various compound objects to be synthesized structurally by object operators. Feature 3 shows that the relations of attribute pairs, class hierarchy and attribute inheritance can be simulated without the need for individual variables.