A Structural Characterization of Extended Correctness-Completeness in Classical Logic
In this paper I deal with first order logic and axiomatic systems. I present the metalogical results that show the property of satisfying Modus Ponens as a necessary and sufficient condition for the extended completeness of the system, and to the Deduction Metatheorem as a necessary and sufficient...
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Universidad Nacional Autónoma de México (UNAM)
2019-01-01
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| Online Access: | https://critica.filosoficas.unam.mx/index.php/critica/article/view/1006 |
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| author | José Alfredo Amor |
| author_facet | José Alfredo Amor |
| author_sort | José Alfredo Amor |
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In this paper I deal with first order logic and axiomatic systems. I present the metalogical results that show the property of satisfying Modus Ponens as a necessary and sufficient condition for the extended completeness of the system, and to the Deduction Metatheorem as a necessary and sufficient condition for the extended correctness of the system. Both supposing that the system satisfies the corresponding restricted properties. These results show that the choice of that rule of inference and of that metatheorem, for any particular axiomatic system, are not a matter of personal liking or of practical convenience, but they play a fundamental role for the extended correctness-completeness properties of the axiomatic system. As a matter of fact, they can be considered as structural properties that characterize the fulfilling of the Extended Correctness and Completeness theorem for the axiomatic system.
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| format | Article |
| id | doaj-art-baecb93dc4514523bae8d03422ca4eaa |
| institution | DOAJ |
| issn | 0011-1503 1870-4905 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Universidad Nacional Autónoma de México (UNAM) |
| record_format | Article |
| series | Crítica |
| spelling | doaj-art-baecb93dc4514523bae8d03422ca4eaa2025-08-20T02:41:20ZengUniversidad Nacional Autónoma de México (UNAM)Crítica0011-15031870-49052019-01-013510310.22201/iifs.18704905e.2003.1006A Structural Characterization of Extended Correctness-Completeness in Classical LogicJosé Alfredo Amor0Facultad de Ciencias Universidad Nacional Autónoma de México In this paper I deal with first order logic and axiomatic systems. I present the metalogical results that show the property of satisfying Modus Ponens as a necessary and sufficient condition for the extended completeness of the system, and to the Deduction Metatheorem as a necessary and sufficient condition for the extended correctness of the system. Both supposing that the system satisfies the corresponding restricted properties. These results show that the choice of that rule of inference and of that metatheorem, for any particular axiomatic system, are not a matter of personal liking or of practical convenience, but they play a fundamental role for the extended correctness-completeness properties of the axiomatic system. As a matter of fact, they can be considered as structural properties that characterize the fulfilling of the Extended Correctness and Completeness theorem for the axiomatic system. https://critica.filosoficas.unam.mx/index.php/critica/article/view/1006logical consequenceaxiomatic systemcompactnesssemantics |
| spellingShingle | José Alfredo Amor A Structural Characterization of Extended Correctness-Completeness in Classical Logic Crítica logical consequence axiomatic system compactness semantics |
| title | A Structural Characterization of Extended Correctness-Completeness in Classical Logic |
| title_full | A Structural Characterization of Extended Correctness-Completeness in Classical Logic |
| title_fullStr | A Structural Characterization of Extended Correctness-Completeness in Classical Logic |
| title_full_unstemmed | A Structural Characterization of Extended Correctness-Completeness in Classical Logic |
| title_short | A Structural Characterization of Extended Correctness-Completeness in Classical Logic |
| title_sort | structural characterization of extended correctness completeness in classical logic |
| topic | logical consequence axiomatic system compactness semantics |
| url | https://critica.filosoficas.unam.mx/index.php/critica/article/view/1006 |
| work_keys_str_mv | AT josealfredoamor astructuralcharacterizationofextendedcorrectnesscompletenessinclassicallogic AT josealfredoamor structuralcharacterizationofextendedcorrectnesscompletenessinclassicallogic |