Matches in SemOpenAlex for { <https://semopenalex.org/work/W1992425561> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W1992425561 endingPage "480" @default.
- W1992425561 startingPage "471" @default.
- W1992425561 abstract "In this paper we consider classes of quantificational formulas specified by restrictions on the number of atomic subformulas appearing in a formula. Little seems to be known about the decision problem for such classes, except that the class whose members contain at most two distinct atomic subformulas is decidable [2]. (We use “decidable” and “undecidable” throughout with respect to satisfiability rather than validity. All undecidable problems to which we refer are of maximal r.e. degree.) The principal result of this paper is the undecidability of the class of those formulas containing five atomic subformulas and with prefixes of the form ∀∃∀…∀. In fact, we show the undecidability of two sub-classes of this class: one (Theorem 1) consists of formulas whose matrices are in disjunctive normal form with two disjuncts; the other (Corollary 1) consists of formulas whose matrices are in conjunctive normal form with three conjuncts. (Theorem 1 sharpens Orevkov's result [8] that the class of formulas in disjunctive normal form with two disjuncts is undecidable.) A second corollary of Theorem 1 shows the undecidability of the class of formulas with prefixes of the form ∀…∀∃, containing six atomic subformulas, and in conjunctive normal form with three conjuncts. These restrictions to prefixes ∀∃∀…∀ and ∀…∀∃ are optimal. For by a result of the first author [5], any class of prenex formulas obtained by restricting both the number of atomic formulas and the number of universal quantifiers is reducible to a finite class of formulas, and so each such class is decidable; and the class of formulas with prefixes ∃…∃∀…∀ is, of course, decidable." @default.
- W1992425561 created "2016-06-24" @default.
- W1992425561 creator A5038375601 @default.
- W1992425561 creator A5046018851 @default.
- W1992425561 date "1973-09-01" @default.
- W1992425561 modified "2023-09-28" @default.
- W1992425561 title "The decision problem for formulas with a small number of atomic subformulas " @default.
- W1992425561 cites W1984820433 @default.
- W1992425561 cites W2486229864 @default.
- W1992425561 doi "https://doi.org/10.2307/2273045" @default.
- W1992425561 hasPublicationYear "1973" @default.
- W1992425561 type Work @default.
- W1992425561 sameAs 1992425561 @default.
- W1992425561 citedByCount "10" @default.
- W1992425561 crossrefType "journal-article" @default.
- W1992425561 hasAuthorship W1992425561A5038375601 @default.
- W1992425561 hasAuthorship W1992425561A5046018851 @default.
- W1992425561 hasConcept C11413529 @default.
- W1992425561 hasConcept C114614502 @default.
- W1992425561 hasConcept C115988155 @default.
- W1992425561 hasConcept C118615104 @default.
- W1992425561 hasConcept C136726353 @default.
- W1992425561 hasConcept C138885662 @default.
- W1992425561 hasConcept C141603448 @default.
- W1992425561 hasConcept C153269930 @default.
- W1992425561 hasConcept C154945302 @default.
- W1992425561 hasConcept C16221470 @default.
- W1992425561 hasConcept C192034797 @default.
- W1992425561 hasConcept C2777212361 @default.
- W1992425561 hasConcept C2780012671 @default.
- W1992425561 hasConcept C33923547 @default.
- W1992425561 hasConcept C41008148 @default.
- W1992425561 hasConcept C41895202 @default.
- W1992425561 hasConcept C6943359 @default.
- W1992425561 hasConceptScore W1992425561C11413529 @default.
- W1992425561 hasConceptScore W1992425561C114614502 @default.
- W1992425561 hasConceptScore W1992425561C115988155 @default.
- W1992425561 hasConceptScore W1992425561C118615104 @default.
- W1992425561 hasConceptScore W1992425561C136726353 @default.
- W1992425561 hasConceptScore W1992425561C138885662 @default.
- W1992425561 hasConceptScore W1992425561C141603448 @default.
- W1992425561 hasConceptScore W1992425561C153269930 @default.
- W1992425561 hasConceptScore W1992425561C154945302 @default.
- W1992425561 hasConceptScore W1992425561C16221470 @default.
- W1992425561 hasConceptScore W1992425561C192034797 @default.
- W1992425561 hasConceptScore W1992425561C2777212361 @default.
- W1992425561 hasConceptScore W1992425561C2780012671 @default.
- W1992425561 hasConceptScore W1992425561C33923547 @default.
- W1992425561 hasConceptScore W1992425561C41008148 @default.
- W1992425561 hasConceptScore W1992425561C41895202 @default.
- W1992425561 hasConceptScore W1992425561C6943359 @default.
- W1992425561 hasIssue "03" @default.
- W1992425561 hasLocation W19924255611 @default.
- W1992425561 hasOpenAccess W1992425561 @default.
- W1992425561 hasPrimaryLocation W19924255611 @default.
- W1992425561 hasRelatedWork W1512359663 @default.
- W1992425561 hasRelatedWork W1538330076 @default.
- W1992425561 hasRelatedWork W1591531250 @default.
- W1992425561 hasRelatedWork W1608133301 @default.
- W1992425561 hasRelatedWork W1976400286 @default.
- W1992425561 hasRelatedWork W2002672992 @default.
- W1992425561 hasRelatedWork W2042347326 @default.
- W1992425561 hasRelatedWork W2046337029 @default.
- W1992425561 hasRelatedWork W2050426366 @default.
- W1992425561 hasRelatedWork W2099158350 @default.
- W1992425561 hasRelatedWork W2122908864 @default.
- W1992425561 hasRelatedWork W2165311764 @default.
- W1992425561 hasRelatedWork W2301389031 @default.
- W1992425561 hasRelatedWork W2502826815 @default.
- W1992425561 hasRelatedWork W2519271719 @default.
- W1992425561 hasRelatedWork W2566393547 @default.
- W1992425561 hasRelatedWork W2652260735 @default.
- W1992425561 hasRelatedWork W2906359945 @default.
- W1992425561 hasRelatedWork W2952193478 @default.
- W1992425561 hasRelatedWork W3048669164 @default.
- W1992425561 hasVolume "38" @default.
- W1992425561 isParatext "false" @default.
- W1992425561 isRetracted "false" @default.
- W1992425561 magId "1992425561" @default.
- W1992425561 workType "article" @default.