This paper deals with algebraic expressions constrained by states for causal relations. Abstracted from procedural and reference data relations, Heyting algebra expressions of some form may be adopted as theoretical basis of a language system with state constrains for data representations. Query operations for such algebraic expressions are presented by 3-valued model theory of algebraic expressions, where the unknown value is available and negatives are used in two ways. Model theory of algebraic expressions is given by both prefixpoint of associated nonmonotonic mappings and predicates of corresponding queries, such that semantics is denotational. As regards state traverses and transitions accompanied by queries at states, algebraic structure is presented in a semiring structure, where alternation for selections of state transitions, and concatenation of state transitions are involved in. Models of algebraic expressions denote queries such that they are organized into sequences on a semiring structure. In terms of model construction and semiring structure, this paper presents data semantics abstracted for state constraint expressions of causal relations.