Abstract
If one wants a good semantic representation of a program over a universe of possible total states, then one needs to consider the paths that are associated with α. Those paths may be divided into two groups: those that correspond to complete computations according to the program and those that do not. The latter group can be further divided into two subgroups: the finite and the infinite. Thus, with each program α, one can associate three sets of paths: (1) H (α) = the set of halt paths, (2) I (α) = the set of infinite paths, and (3) F(α) = the set of fail paths. In this way, each program α defines what might be called a “signature (H(α), I(α), F(α)). Two kinds of semantics are discussed: path semantics and relational semantics. The expressions of the formal language are divided into two distinct categories—namely, terms and formulae, which are interrelated in intricate ways. The chapter also discusses Fischer/Ladner closure.
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