A Proof Theory for General Unification:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1991
|
| Schriftenreihe: | Progress in Computer Science and Applied Logic
11 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems |
| Beschreibung: | 1 Online-Ressource (VII, 178 p) |
| ISBN: | 9781461204350 9781461267584 |
| DOI: | 10.1007/978-1-4612-0435-0 |
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| 500 | |a In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems | ||
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Datensatz im Suchindex
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| discipline | Informatik Mathematik |
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| isbn | 9781461204350 9781461267584 |
| language | English |
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| spelling | Snyder, Wayne Verfasser aut A Proof Theory for General Unification by Wayne Snyder Boston, MA Birkhäuser Boston 1991 1 Online-Ressource (VII, 178 p) txt rdacontent c rdamedia cr rdacarrier Progress in Computer Science and Applied Logic 11 In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems Computer science Information theory Logic, Symbolic and mathematical Computer Science Theory of Computation Mathematical Logic and Foundations Informatik Unifikationstheorie (DE-588)4186894-8 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf Unifikationstheorie (DE-588)4186894-8 s Beweistheorie (DE-588)4145177-6 s 1\p DE-604 Automatisches Beweisverfahren (DE-588)4069034-9 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-0435-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Snyder, Wayne A Proof Theory for General Unification Computer science Information theory Logic, Symbolic and mathematical Computer Science Theory of Computation Mathematical Logic and Foundations Informatik Unifikationstheorie (DE-588)4186894-8 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4186894-8 (DE-588)4069034-9 (DE-588)4145177-6 |
| title | A Proof Theory for General Unification |
| title_auth | A Proof Theory for General Unification |
| title_exact_search | A Proof Theory for General Unification |
| title_full | A Proof Theory for General Unification by Wayne Snyder |
| title_fullStr | A Proof Theory for General Unification by Wayne Snyder |
| title_full_unstemmed | A Proof Theory for General Unification by Wayne Snyder |
| title_short | A Proof Theory for General Unification |
| title_sort | a proof theory for general unification |
| topic | Computer science Information theory Logic, Symbolic and mathematical Computer Science Theory of Computation Mathematical Logic and Foundations Informatik Unifikationstheorie (DE-588)4186894-8 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Computer science Information theory Logic, Symbolic and mathematical Computer Science Theory of Computation Mathematical Logic and Foundations Informatik Unifikationstheorie Automatisches Beweisverfahren Beweistheorie |
| url | https://doi.org/10.1007/978-1-4612-0435-0 |
| work_keys_str_mv | AT snyderwayne aprooftheoryforgeneralunification |