Peano Arithmetic as Axiomatization of the Time Frame in Logics of Programs and in Dynamic Logics

Abstract Biro, B. and I. Sain, Peano arithmetic as axiomatization of the time frame in logics of programs and in dynamic logics, Annals of Pure and Applied Logic 63 (1993) 201-225. We show that one can prove the partial correctness of more programs using Peano's axioms for the time frames of three-sorted time models than using only Presburger's axioms, that is it is useful to allow multiplication of time points at program verification and in dynamic and temporal logics. We organized the paper as follows: 1. Preliminaries, 2. The main result, 3. Peano arithmetic with bounded multiplication, 4. Connections with temporal logics and dynamic logics, Acknowledgements, References.

[1]  Ildikó Sain.  Total Correctness in Nonstandard Logics of Programs , 1987, Theor. Comput. Sci..

[2]  Ildikó Sain.  Structured Nonstandard Dynamic Logic , 1984, Math. Log. Q..

[3]  Ildikó Sain,et al.  Completeness Problems in Verification of Programs and Program Schemes , 1979, MFCS.

[4]  Ildikó Sain.  Temporal Logics Need Their Clocks , 1992, Theor. Comput. Sci..

[5]  Gauri Viswanathan.  Some other time: Review of Time and the Other: How Anthropology Makes its Object by Johannes Fabian. New York: Columbia University Press, 1983. , 1986 .

[6]  Leszek Pacholski,et al.  Model theory of algebra and arithmetic , 1980 .

[7]  Ildikó Sain,et al.  A Complete Logic for Reasoning about Programs via Nonstandard Model Theory I , 1982, Theor. Comput. Sci..

[8]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[9]  A. Salwicki.  Logics of Programs and Their Applications , 1980, Lecture Notes in Computer Science.

[10]  Martín Abadi,et al.  The Power of Temporal Proofs , 1989, Theor. Comput. Sci..

[11]  Ildikó Sain.  Comparing and characterising the powers of established program verification methods , 1993 .

[12]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[13]  Martín Abadi,et al.  The power of temporal proofs (corrigendum) , 1990 .

[14]  Peter Øhrstrøm,et al.  Temporal Logic , 1994, Lecture Notes in Computer Science.

[15]  Jeff B. Paris,et al.  A Hierarchy of Cuts in Models of Arithmetic , 1980 .

[16]  Petr Hájek,et al.  A simple dynamic logic , 1986, Theor. Comput. Sci..

[17]  Ildikó Sain,et al.  On the Strength of Temporal Proofs , 1989, Theor. Comput. Sci..

[18]  Hajnal Andréka.  Sharpening the characterization of the power of Floyd method , 1980, Logic of Programs.

[19]  Ildikó Sain,et al.  Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs? , 1988, Stud Logica.

[20]  István Németi,et al.  Nonstandard Dynamic Logic , 1981, Logic of Programs.

[21]  J. Paris,et al.  ∑n-Collection Schemas in Arithmetic , 1978 .

[22]  Ildikó Sain,et al.  On the Strength of Temporal Proofs , 1989, MFCS.

[23]  Tamás Gergely,et al.  First-Order Programming Theories , 1991, EATCS Monographs on Theoretical Computer Science.