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abstract abstract data structure Algebraic Semantics algorithmic formula Algorithmic Logic algorithmic theory annotation arity axioms Boolean called classical quantifiers common firing rule completeness theorem Computer Science computing agents consequence operation consider construction contains counter machines data structure type data structure variables decl defined definition dynamic logic elements equivalent event-sequences example execution expressions file descriptor finite formal function GDISPLAY global instructions Hence induction infinite integer Lecture Notes Lemma logics of programs Loop Invariant Maximum Firing Strategy modal logic model theory natural numbers nonstandard notation object obtain occur partial correctness Petri nets predicate pref prefixing procedure processor program schemes program verification programming language programming system proof concept propositional provable prove QPDL recursive relation result rules of inference satisfied sequence similarity type Simula 67 simulate SL chain subset symbols syntactic termination tion total correctness tree valuation vectors of values