The calculus of facts
Nets of conditions and events (‘special’ Petri nets) are widely used models of dynamic systems. They represent the causal structure of the concurrent operation and co-operation of the components of a system. In this paper we introduce a net theoretic version of the first-order predicate calculus. Its purpose is to offer a formal language for expressing the relationship between a net model and the modelled system, and to provide rules for deriving the logical consequences of such an interpretation in a way that the results are expressed in the same language as the model, namely the net language. By this we permit the use of symbolic logic as part of a general formalism for the analysis and specification of dynamic systems. We show how ‘static’ logic can be correctly applied even in those practically important dynamic contexts where certain sentences change their truthvalues in a not fully specified order. As a useful by-product the graphical representation of nets induces a very natural graphical representation of the predicate calculus.
KeywordsMutual Exclusion Conjunctive Normal Form Derivation Rule Atomic Sentence Resolution Rule
Unable to display preview. Download preview PDF.
- 1.Petri,C.A.: Interpretations of Net Theory. Internal Report ISF-75-07, GMD Bonn (1975)Google Scholar
- 2.Thieler-Mevissen,G.: The Petri Net Calculus of Predicate Logic. Internal Report (in preparation), GMD Bonn (1976)Google Scholar
- 3.Chang,C; Lee,R.: Symbolic Logic and Automated Theorem Proving. Academic Press, New York and London (1973)Google Scholar