Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
An axiomatic basis for computer programming
Communications of the ACM
A Discipline of Programming
A complete axiomatic system for proving deductions about recursive programs
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
ICSE '76 Proceedings of the 2nd international conference on Software engineering
Strong verification of programs
IEEE Transactions on Software Engineering
Non-standard algorithmic and dynamic logic
Journal of Symbolic Computation
Journal of the ACM (JACM)
Skinny and fleshy failures of relative completeness
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Meager and replete failures of relative completeness
Journal of the ACM (JACM)
Algebraic approaches to nondeterminism—an overview
ACM Computing Surveys (CSUR)
Axiomatic Definitions of Programming Languages: A Theoretical Assessment
Journal of the ACM (JACM)
Specifying the Semantics of while Programs: A Tutorial and Critique of a Paper by Hoare and Lauer
ACM Transactions on Programming Languages and Systems (TOPLAS)
Nondeterminism in logics of programs
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Axiomatic definitions of programming languages: a theoretical assessment (preliminary report)
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Axiomatic definitions of programming languages, II
POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Recursion in logics of programs
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Specifying programming language semantics: a tutorial and critique of a paper by Hoare and Lauer
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Axiomatic definability and completeness for recursive programs
POPL '82 Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A complete axiomatic system for proving deductions about recursive programs
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
A practical decision method for propositional dynamic logic (Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On the Completeness of Dynamic Logic
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Boolean and classical restriction categories
Mathematical Structures in Computer Science
A proof-checker for dynamic logic
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Halting and equivalence of program schemes in models of arbitrary theories
Fields of logic and computation
The Complete Proof Theory of Hybrid Systems
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Logical analysis of hybrid systems: a complete answer to a complexity challenge
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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Dynamic logic is a generalization of first order logic in which quantifiers of the form “for all &khgr;...” are replaced by phrases of the form “after executing program &agr;...”. This logic subsumes most existing first-order logics of programs that manipulate their environment, including Floyd's and Hoare's logics of partial correctness and Manna and Waldinger's logic of total correctness, yet is more closely related to classical first-order logic than any other proposed logic of programs. We consider two issues: how hard is the validity problem for the formulae of dynamic logic, and how might one axiomatize dynamic logic? We give bounds on the validity problem for some special cases, including a &Pgr;02-completeness result for the partial correctness theories of uninterpreted flowchart programs. We also demonstrate the completeness of an axiomatization of dynamic logic relative to arithmetic.