Theoretical Basis of Language System with State Constraints

Abstract

: This paper presents theoretical basis of a language system whose program is described as algebraic expressions and implemented as abstract state machine. The behaviors of the described expressions may be captured (with their models) as causing sequences for state transitions, where composition and alternation for state transitions are mechanized in algebraic structure. Monitoring facilities to the language system may be described with state concepts, as well. With respect to intuitionistic logic and logical program containing negatives, Heyting algebra expressions are taken rather than already established nonmonotonic reasoning programs with negations, where 3-valued domain may be of use for the undefined to be allowable such that positives and negatives may be consistently evaluated, instead of rigid 2-valued settlements. We may have a standard form of Heyting algebra expressions in accordance to logical and AI programming, where the expressions are constrained with states. The states may be regarded as environmental conditions or objects as in object-oriented programming. As regards 3-valued models of given expressions, monotonic mapping cannot be in general as-sociated with, but some ways are presented to approximate fixed points of a mapping for the given expression. Then the formal description of programs may be given with reference to state transitions, which is thought of as proposing a language system structure.