Definability in partial logic: the propositional part
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Tilburg
1990
|
| Schriftenreihe: | Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report
24 |
| Schlagwörter: | |
| Abstract: | Abstract: "This paper addresses to definability (or, more precisely, relative functional completeness) in partial logic with respect to conditions on the set of truth functions. Well-known condition in this area are monotonicity and classical closure. Some isolated definability results are known, whereas other plausible questions have not been answered yet. The aim of this paper is simply to fill in some of these gaps. To this purpose we first present a general framework and the key notion of a closed class and definability w.r.t. a closed class This machinery can be used to show that all is not gold that glitters: distributivity, though attractive since it defines extensions of the standard connectives, is not definable. Next the relevant connectives and conditions are discussed. Some 'new' conditions are proposed or formalized (such as general closure, preservation of dualization, freedom) and one new operator is introduced: dual negation ([symbol]), which is the dual of standard negation. This leads to a number of new definability results for the 3- and the 4-valued case The paper also contain a first discussion of the relative strength of the different conditions, by comparison of the number of functions of certain arity single out by a given set of conditions. E.g., it is shown that the number of n-ary monotone quadrivalent functions is the square of the number of increasing generalized quantifiers over a domain of 2n individuals. The appendix treats the (to our knowledge) new subject of Sheffer functions for closed classes. Perhaps most surprising here are some negative results: the existence of closed classes which can not be defined by a single connective. |
| Beschreibung: | Teilw. zugl.: Tilburg, Univ., Diss. |
| Umfang: | 42 S. |
Internformat
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| 100 | 1 | |a Thijsse, Elias |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Definability in partial logic |b the propositional part |c Elias Thijsse |
| 264 | 1 | |a Tilburg |c 1990 | |
| 300 | |a 42 S. | ||
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| 490 | 1 | |a Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report |v 24 | |
| 500 | |a Teilw. zugl.: Tilburg, Univ., Diss. | ||
| 520 | 3 | |a Abstract: "This paper addresses to definability (or, more precisely, relative functional completeness) in partial logic with respect to conditions on the set of truth functions. Well-known condition in this area are monotonicity and classical closure. Some isolated definability results are known, whereas other plausible questions have not been answered yet. The aim of this paper is simply to fill in some of these gaps. To this purpose we first present a general framework and the key notion of a closed class and definability w.r.t. a closed class | |
| 520 | 3 | |a This machinery can be used to show that all is not gold that glitters: distributivity, though attractive since it defines extensions of the standard connectives, is not definable. Next the relevant connectives and conditions are discussed. Some 'new' conditions are proposed or formalized (such as general closure, preservation of dualization, freedom) and one new operator is introduced: dual negation ([symbol]), which is the dual of standard negation. This leads to a number of new definability results for the 3- and the 4-valued case | |
| 520 | 3 | |a The paper also contain a first discussion of the relative strength of the different conditions, by comparison of the number of functions of certain arity single out by a given set of conditions. E.g., it is shown that the number of n-ary monotone quadrivalent functions is the square of the number of increasing generalized quantifiers over a domain of 2n individuals. The appendix treats the (to our knowledge) new subject of Sheffer functions for closed classes. Perhaps most surprising here are some negative results: the existence of closed classes which can not be defined by a single connective. | |
| 650 | 4 | |a Logic | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 830 | 0 | |a Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report |v 24 |w (DE-604)BV005294686 |9 24 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-003306001 | |
Datensatz im Suchindex
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| author | Thijsse, Elias |
| author_facet | Thijsse, Elias |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
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| id | DE-604.BV005294778 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:31:14Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003306001 |
| oclc_num | 25393663 |
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| physical | 42 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
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| series | Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report |
| series2 | Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report |
| spelling | Thijsse, Elias Verfasser aut Definability in partial logic the propositional part Elias Thijsse Tilburg 1990 42 S. txt rdacontent n rdamedia nc rdacarrier Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report 24 Teilw. zugl.: Tilburg, Univ., Diss. Abstract: "This paper addresses to definability (or, more precisely, relative functional completeness) in partial logic with respect to conditions on the set of truth functions. Well-known condition in this area are monotonicity and classical closure. Some isolated definability results are known, whereas other plausible questions have not been answered yet. The aim of this paper is simply to fill in some of these gaps. To this purpose we first present a general framework and the key notion of a closed class and definability w.r.t. a closed class This machinery can be used to show that all is not gold that glitters: distributivity, though attractive since it defines extensions of the standard connectives, is not definable. Next the relevant connectives and conditions are discussed. Some 'new' conditions are proposed or formalized (such as general closure, preservation of dualization, freedom) and one new operator is introduced: dual negation ([symbol]), which is the dual of standard negation. This leads to a number of new definability results for the 3- and the 4-valued case The paper also contain a first discussion of the relative strength of the different conditions, by comparison of the number of functions of certain arity single out by a given set of conditions. E.g., it is shown that the number of n-ary monotone quadrivalent functions is the square of the number of increasing generalized quantifiers over a domain of 2n individuals. The appendix treats the (to our knowledge) new subject of Sheffer functions for closed classes. Perhaps most surprising here are some negative results: the existence of closed classes which can not be defined by a single connective. Logic (DE-588)4113937-9 Hochschulschrift gnd-content Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report 24 (DE-604)BV005294686 24 |
| spellingShingle | Thijsse, Elias Definability in partial logic the propositional part Instituut voor Taal- en Kennistechnologie <Tilburg>: ITK research report Logic |
| subject_GND | (DE-588)4113937-9 |
| title | Definability in partial logic the propositional part |
| title_auth | Definability in partial logic the propositional part |
| title_exact_search | Definability in partial logic the propositional part |
| title_full | Definability in partial logic the propositional part Elias Thijsse |
| title_fullStr | Definability in partial logic the propositional part Elias Thijsse |
| title_full_unstemmed | Definability in partial logic the propositional part Elias Thijsse |
| title_short | Definability in partial logic |
| title_sort | definability in partial logic the propositional part |
| title_sub | the propositional part |
| topic | Logic |
| topic_facet | Logic Hochschulschrift |
| volume_link | (DE-604)BV005294686 |
| work_keys_str_mv | AT thijsseelias definabilityinpartiallogicthepropositionalpart |