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Results on the propositional \(\mu\)-calculus. (English) Zbl 0553.03007
In this paper we define and study a propositional \(\mu\)-calculus \(L\mu\), which consists essentially of propositional modal logic with a least fixpoint operator. \(L\mu\) is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL). For a restricted version we give an exponential-time decision procedure, small model property, and complete deductive system, thereby subsuming the corresponding results for PDL.

MSC:
03B45 Modal logic (including the logic of norms)
68Q65 Abstract data types; algebraic specification
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[1] De Bakker, J.W., Mathematical theory of program correctness, (1980), Prentice-Hall Englewood Cliffs, NJ
[2] De Bakker, J.W.; De Roever, W., A calculus for recursive program schemes, (), 167-196 · Zbl 0238.68006
[3] Chandra, A.; Kozen, D.; Stockmeyer, L., Alternation, J. assoc. comput. Mach., 28, 1, 114-133, (1981) · Zbl 0473.68043
[4] Emerson, E.A.; Clarke, E.M., Characterizing correctness properties of parallel programs using fixpoints, (), 169-181 · Zbl 0456.68016
[5] Emerson, E.A.; Clarke, E.M., Design and synthesis of synchronization skeletons using branching-time temporal logic, (), 52-71
[6] Fischer, M.; Ladner, R., Propositional dynamic logic of regular programs, J. comput. system sci., 18, 2, 194-211, (1979) · Zbl 0408.03014
[7] Hitchcock, P.; Park, D.M.R., Induction rules and termination proofs, (), 225-251
[8] Halpern, J.; Reif, J., The propositional dynamic logic of deterministic, well-structured programs (extended abstract), Proc. 22nd IEEE symp. on foundations of computer science, 322-334, (1981)
[9] Kozen, D., A representation theorem for models of ∗-free PDL, (), 352-362
[10] Kozen, D., On the duality of dynamic algebras and Kripke models, (), 1-11
[11] Kozen, D., On induction vs. ∗-continuity, (), 167-176
[12] D. Kozen, On the expressiveness of μ, Unpublished manuscript.
[13] D. Kozen, Small models for the propositional μ-calculus, Unpublished manuscript.
[14] Kozen, D., Results on the propositional μ-calculus, Proc. 9th internat. colloq. on automata, languages, and programming, 348-359, (1982)
[15] Kozen, D.; Parikh, R., An elementary proof of the completeness of PDL, Theoret. comput. sci., 14, 113-118, (1981) · Zbl 0451.03006
[16] Kozen, D.; Parikh, R., A decision procedure for the propositional μ-calculus, () · Zbl 0564.03012
[17] Park, D.M.R, Fixpoint induction and proof of program semantics, (), 59-78 · Zbl 0219.68007
[18] Pratt, V.R., A near optimal method for reasoning about action, J. comput. systems sci., 20, 231-254, (1980) · Zbl 0424.03010
[19] Pratt, V.R., A decidable μ-calculus, Proc. 22nd IEEE symp. on foundations of computer science, 421-427, (1981), (Preliminary Rept.)
[20] De Roever, W.P., Recursive program schemes: semantics and proof theory, () · Zbl 0344.68001
[21] Streett, R., Propositional dynamic logic of looping and converse, Proc. 13th ACM symp. on theory of computing, 375-383, (1981)
[22] Scott, D.; De Bakker, J.W., A theory of programs, (1969), IBM Vienna, Unpublished manuscript
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