Matches in SemOpenAlex for { <https://semopenalex.org/work/W2042347326> ?p ?o ?g. }
Showing items 1 to 70 of
70
with 100 items per page.
- W2042347326 endingPage "424" @default.
- W2042347326 startingPage "399" @default.
- W2042347326 abstract "Abstract We give resource bounded versions of the Completeness Theorem for propositional and predicate logic. For example, it is well known that every computable consistent propositional theory has a computable complete consistent extension. We show that, when length is measured relative to the binary representation of natural numbers and formulas, every polynomial time decidable propositional theory has an exponential time ( EXPTIME ) complete consistent extension whereas there is a nondeterministic polynomial time ( NP ) decidable theory which has no polynomial time complete consistent extension when length is measured relative to the binary representation of natural numbers and formulas. It is well known that a propositional theory is axiomatizable (respectively decidable) if and only if it may be represented as the set of infinite paths through a computable tree (respectively a computable tree with no dead ends). We show that any polynomial time decidable theory may be represented as the set of paths through a polynomial time decidable tree. On the other hand, the statement that every polynomial time decidable tree represents the set of complete consistent extensions of some theory which is polynomial time decidable, relative to the tally representation of natural numbers and formulas, is equivalent to P = NP . For predicate logic, we develop a complexity theoretic version of the Henkin construction to prove a complexity theoretic version of the Completeness Theorem. Our results imply that that any polynomial space decidable theory Δ possesses a polynomial space computable model which is exponential space decidable and thus Δ has an exponential space complete consistent extension. Similar results are obtained for other notions of complexity." @default.
- W2042347326 created "2016-06-24" @default.
- W2042347326 creator A5057979748 @default.
- W2042347326 creator A5090907219 @default.
- W2042347326 date "2006-06-01" @default.
- W2042347326 modified "2023-09-23" @default.
- W2042347326 title "Complexity, decidability and completeness" @default.
- W2042347326 cites W1488688643 @default.
- W2042347326 cites W1513644114 @default.
- W2042347326 cites W1545819195 @default.
- W2042347326 cites W187439451 @default.
- W2042347326 cites W1975119571 @default.
- W2042347326 cites W2013547557 @default.
- W2042347326 cites W2016668436 @default.
- W2042347326 cites W2054338826 @default.
- W2042347326 cites W2056895958 @default.
- W2042347326 cites W2112105484 @default.
- W2042347326 cites W2166717942 @default.
- W2042347326 cites W4232277851 @default.
- W2042347326 cites W4242467785 @default.
- W2042347326 cites W56322521 @default.
- W2042347326 cites W1594476753 @default.
- W2042347326 doi "https://doi.org/10.2178/jsl/1146620150" @default.
- W2042347326 hasPublicationYear "2006" @default.
- W2042347326 type Work @default.
- W2042347326 sameAs 2042347326 @default.
- W2042347326 citedByCount "1" @default.
- W2042347326 countsByYear W20423473262019 @default.
- W2042347326 crossrefType "journal-article" @default.
- W2042347326 hasAuthorship W2042347326A5057979748 @default.
- W2042347326 hasAuthorship W2042347326A5090907219 @default.
- W2042347326 hasConcept C11413529 @default.
- W2042347326 hasConcept C114614502 @default.
- W2042347326 hasConcept C118615104 @default.
- W2042347326 hasConcept C153269930 @default.
- W2042347326 hasConcept C176181172 @default.
- W2042347326 hasConcept C179799912 @default.
- W2042347326 hasConcept C197685441 @default.
- W2042347326 hasConcept C311688 @default.
- W2042347326 hasConcept C33923547 @default.
- W2042347326 hasConceptScore W2042347326C11413529 @default.
- W2042347326 hasConceptScore W2042347326C114614502 @default.
- W2042347326 hasConceptScore W2042347326C118615104 @default.
- W2042347326 hasConceptScore W2042347326C153269930 @default.
- W2042347326 hasConceptScore W2042347326C176181172 @default.
- W2042347326 hasConceptScore W2042347326C179799912 @default.
- W2042347326 hasConceptScore W2042347326C197685441 @default.
- W2042347326 hasConceptScore W2042347326C311688 @default.
- W2042347326 hasConceptScore W2042347326C33923547 @default.
- W2042347326 hasIssue "2" @default.
- W2042347326 hasLocation W20423473261 @default.
- W2042347326 hasOpenAccess W2042347326 @default.
- W2042347326 hasPrimaryLocation W20423473261 @default.
- W2042347326 hasRelatedWork W1973386461 @default.
- W2042347326 hasRelatedWork W2012572971 @default.
- W2042347326 hasRelatedWork W2013091420 @default.
- W2042347326 hasRelatedWork W2075449032 @default.
- W2042347326 hasRelatedWork W2166566648 @default.
- W2042347326 hasRelatedWork W2415632638 @default.
- W2042347326 hasRelatedWork W2421475109 @default.
- W2042347326 hasRelatedWork W2595899102 @default.
- W2042347326 hasRelatedWork W2963209704 @default.
- W2042347326 hasRelatedWork W4297792110 @default.
- W2042347326 hasVolume "71" @default.
- W2042347326 isParatext "false" @default.
- W2042347326 isRetracted "false" @default.
- W2042347326 magId "2042347326" @default.
- W2042347326 workType "article" @default.