Reasoning with first order nondeterministic specifications
Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Konikowska, Beata [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1999 |
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| Schlagwörter: |
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| Systematik: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 1999 |
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| Übergeordnetes Werk: |
Enthalten in: Acta informatica - Springer-Verlag, 1971, 36(1999), 5 vom: Sept., Seite 375-403 |
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| Übergeordnetes Werk: |
volume:36 ; year:1999 ; number:5 ; month:09 ; pages:375-403 |
| Links: |
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| DOI / URN: |
10.1007/s002360050165 |
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| Katalog-ID: |
OLC2056517949 |
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| 520 | |a Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. | ||
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10.1007/s002360050165 doi (DE-627)OLC2056517949 (DE-He213)s002360050165-p DE-627 ger DE-627 rakwb eng 050 VZ 24,1 ssgn SA 1220 VZ rvk Konikowska, Beata verfasserin aut Reasoning with first order nondeterministic specifications 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. Alternate Solution Order Logic Deduction System Atomic Formula Natural Deduction Białasik, Marcin aut Enthalten in Acta informatica Springer-Verlag, 1971 36(1999), 5 vom: Sept., Seite 375-403 (DE-627)129288179 (DE-600)120032-X (DE-576)014469766 0001-5903 nnns volume:36 year:1999 number:5 month:09 pages:375-403 https://doi.org/10.1007/s002360050165 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-BBI GBV_ILN_11 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4325 GBV_ILN_4700 SA 1220 AR 36 1999 5 09 375-403 |
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10.1007/s002360050165 doi (DE-627)OLC2056517949 (DE-He213)s002360050165-p DE-627 ger DE-627 rakwb eng 050 VZ 24,1 ssgn SA 1220 VZ rvk Konikowska, Beata verfasserin aut Reasoning with first order nondeterministic specifications 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. Alternate Solution Order Logic Deduction System Atomic Formula Natural Deduction Białasik, Marcin aut Enthalten in Acta informatica Springer-Verlag, 1971 36(1999), 5 vom: Sept., Seite 375-403 (DE-627)129288179 (DE-600)120032-X (DE-576)014469766 0001-5903 nnns volume:36 year:1999 number:5 month:09 pages:375-403 https://doi.org/10.1007/s002360050165 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-BBI GBV_ILN_11 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4325 GBV_ILN_4700 SA 1220 AR 36 1999 5 09 375-403 |
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10.1007/s002360050165 doi (DE-627)OLC2056517949 (DE-He213)s002360050165-p DE-627 ger DE-627 rakwb eng 050 VZ 24,1 ssgn SA 1220 VZ rvk Konikowska, Beata verfasserin aut Reasoning with first order nondeterministic specifications 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. Alternate Solution Order Logic Deduction System Atomic Formula Natural Deduction Białasik, Marcin aut Enthalten in Acta informatica Springer-Verlag, 1971 36(1999), 5 vom: Sept., Seite 375-403 (DE-627)129288179 (DE-600)120032-X (DE-576)014469766 0001-5903 nnns volume:36 year:1999 number:5 month:09 pages:375-403 https://doi.org/10.1007/s002360050165 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-BBI GBV_ILN_11 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4325 GBV_ILN_4700 SA 1220 AR 36 1999 5 09 375-403 |
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10.1007/s002360050165 doi (DE-627)OLC2056517949 (DE-He213)s002360050165-p DE-627 ger DE-627 rakwb eng 050 VZ 24,1 ssgn SA 1220 VZ rvk Konikowska, Beata verfasserin aut Reasoning with first order nondeterministic specifications 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. Alternate Solution Order Logic Deduction System Atomic Formula Natural Deduction Białasik, Marcin aut Enthalten in Acta informatica Springer-Verlag, 1971 36(1999), 5 vom: Sept., Seite 375-403 (DE-627)129288179 (DE-600)120032-X (DE-576)014469766 0001-5903 nnns volume:36 year:1999 number:5 month:09 pages:375-403 https://doi.org/10.1007/s002360050165 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-BBI GBV_ILN_11 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4325 GBV_ILN_4700 SA 1220 AR 36 1999 5 09 375-403 |
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10.1007/s002360050165 doi (DE-627)OLC2056517949 (DE-He213)s002360050165-p DE-627 ger DE-627 rakwb eng 050 VZ 24,1 ssgn SA 1220 VZ rvk Konikowska, Beata verfasserin aut Reasoning with first order nondeterministic specifications 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. Alternate Solution Order Logic Deduction System Atomic Formula Natural Deduction Białasik, Marcin aut Enthalten in Acta informatica Springer-Verlag, 1971 36(1999), 5 vom: Sept., Seite 375-403 (DE-627)129288179 (DE-600)120032-X (DE-576)014469766 0001-5903 nnns volume:36 year:1999 number:5 month:09 pages:375-403 https://doi.org/10.1007/s002360050165 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-BBI GBV_ILN_11 GBV_ILN_24 GBV_ILN_31 GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2190 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4325 GBV_ILN_4700 SA 1220 AR 36 1999 5 09 375-403 |
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Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. © Springer-Verlag Berlin Heidelberg 1999 |
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Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. © Springer-Verlag Berlin Heidelberg 1999 |
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Abstract. The paper presents a variant of first order logic for specifying nondeterministic software. Models of the logics are multialgebras, i.e. multi-sorted algebras with set-valued operations, together with multi-sorted valuations of variables. We allow empty carrier sets but the valuations are kept total. Terms are interpreted as sets and the usual set of algebraic terms is extended by an additional ${\sf let}$ construct used for limiting nondeterminism. Atomic formulae are of the form $t_1 \to t_2$ where $\to$ is a rewrite operator, corresponding semantically to inclusion. For the above logic, we develop two complete deduction systems in the natural deduction style: a Rasiowa-Sikorski system for sequences of formulae, and a cut-free Gentzen-style sequent calculus. We also consider the issues of determinism and partiality, proposing alternate solutions to defining the respective predicates in our logic. © Springer-Verlag Berlin Heidelberg 1999 |
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