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Criterion for propositional calculi to be finitely generated
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G. V. Bokov
Published/Copyright:
May 1, 2014
Abstract
The paper is concerned with propositional calculi having arbitrary modus inference operations that are analogous to the modus ponens operation. For these calculi the question on the existence and cardinality of sets of generators is examined. A criterion for propositional calculi with arbitrary modus inference operations to be finitely generated is put forward. For some calculi, the existence of a finite complete system of tautologies is shown to imply the existence of a basis of arbitrarily large finite cardinality. We show the existence of propositional calculi with countable basis, without any basis, and calculi having a complete subsystem without any basis.
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Published Online: 2014-5-1
Published in Print: 2013-12-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
Keywords for this article
Keywords
Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
