By Franz Kurfeß (auth.)
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Extra resources for Parallelism in Logic: Its Potential for Performance and Program Development
Computational Evaluation The truth value of a particular formula can be determined by applying semantic rules according to the operators defining the structure of the formula. A satisfying way of evaluating smaller sentences is given by truth tables. For larger sentences, the inspection of the corresponding semantic tree usually is better suited. In principle, a complete analysis of all possible truth value assignments can be made to decide if a formula is valid or not; efficiency reasons, however, usually ask for more sophisticated methods.
Thus, an interpretation I is based on a domain V, and the set of objects of V together with functions and relations over V provide a meaning for constant, (free) variable, function and predicate symbols. With such an interpretation I we can determine the value of a formula :F (which is either true or false) or of a term T (which must be an object in the domain V). The value of a complicated expression is determined stepwise by applying the appropriate semantical rules. Properties of Sentences The most important properties of sentences are basically the same as in propositional logic: Satisfiability: An interpretation I for a formula:F can be found such that :F is true; Validity: :F is true for any interpretation I.
A quantified assignment denotes zero or more components; these components are made explicit by instantiating the bound variables of the variable list, one component for each instance. 2 Parallelism: UNITY and Processes 39 What has been clarified by now is the structure of (maybe complex) assignments; such an assignment is executed by evaluating the righthand sides of all its components simultaneously and assigning the resulting values to the variables on the left-hand side. Statements in a UNITY program are used to group correlated assignments and isolate independent ones; statements are separated by the symbol ~, and may be quantified in the same way as a quantified assignment, using ~ instead of II: ~ (i : 0 ~ i ~ n :: Ai := Ai * Bi).