Communicating sequential processes
Communicating sequential processes
Computer viruses: theory and experiments
Computers and Security
Communications of the ACM
Process algebra
McCarthy algebras: a model of McCarthy's logical calculus
Fundamenta Informaticae
Kleen's three-valued logic and process algebra
Information Processing Letters
Introduction to Process Algebra
Introduction to Process Algebra
Thread algebra for strategic interleaving
Formal Aspects of Computing
Belnap's logic and conditional composition
Theoretical Computer Science
Risk Assessment for One-Counter Threads
Theory of Computing Systems
A bypass of cohen's impossibility result
EGC'05 Proceedings of the 2005 European conference on Advances in Grid Computing
Proposition algebra and short-circuit logic
FSEN'11 Proceedings of the 4th IPM international conference on Fundamentals of Software Engineering
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Sequential propositional logic deviates from conventional propositional logic by taking into account that during the sequential evaluation of a propositional statement, atomic propositions may yield different Boolean values at repeated occurrences. We introduce “free valuations” to capture this dynamics of a propositional statement's environment. The resulting logic is phrased as an equationally specified algebra rather than in the form of proof rules, and is named “proposition algebra.” It is strictly more general than Boolean algebra to the extent that the classical connectives fail to be expressively complete in the sequential case. The four axioms for free valuation congruence are then combined with other axioms in order define a few more valuation congruences that gradually identify more propositional statements, up to static valuation congruence (which is the setting of conventional propositional logic). Proposition algebra is developed in a fashion similar to the process algebra ACP and the program algebra PGA, via an algebraic specification which has a meaningful initial algebra for which a range of coarser congruences are considered important as well. In addition, infinite objects (i.e., propositional statements, processes and programs respectively) are dealt with by means of an inverse limit construction which allows the transfer of knowledge concerning finite objects to facts about infinite ones while reducing all facts about infinite objects to an infinity of facts about finite ones in return.