Matches in SemOpenAlex for { <https://semopenalex.org/work/W2106630772> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W2106630772 endingPage "442" @default.
- W2106630772 startingPage "439" @default.
- W2106630772 abstract "§1. A complete atomic modal algebra (CAMA) is a complete atomic Boolean algebra with an additional completely additive unary operator. A (Kripke) frame is just a binary relation on a nonempty set. If is a frame, then is a CAMA, where mX = { y ∣ (∃ x )( y < x Є X )}; and if is a CAMA then is a frame, where is the set of atoms of and b 1 < b 2 ⇔ b 1 ∩ mb 2 ≠∅. Now , and the validity of a modal formula on is equivalent to the satisfaction of a modal algebra polynomial identity by and conversely, so the validity-preserving constructions on frames ought to be in some sense equivalent to the identity-preserving constructions on CAMA's. The former are important for modal logic, and many of the results of universal algebra apply to the latter, so it is worthwhile to fix precisely the sense of the equivalence. The most important identity-preserving constructions on CAMA's can be described in terms of homomorphisms and complete homomorphisms. Let and be the categories of CAMA's with homomorphisms and complete homomorphisms, respectively. We shall define categories and of frames with appropriate morphisms, and show them to be dual respectively to and . Then we shall consider certain identity-preserving constructions on CAMA's and attempt to describe the corresponding validity-preserving constructions on frames. The proofs of duality involve some rather detailed calculations, which have been omitted. All the category theory a reader needs to know is in the first twenty pages of [7]." @default.
- W2106630772 created "2016-06-24" @default.
- W2106630772 creator A5045940955 @default.
- W2106630772 date "1975-09-01" @default.
- W2106630772 modified "2023-09-24" @default.
- W2106630772 title "Categories of frames for modal logic" @default.
- W2106630772 cites W2046750700 @default.
- W2106630772 doi "https://doi.org/10.2307/2272167" @default.
- W2106630772 hasPublicationYear "1975" @default.
- W2106630772 type Work @default.
- W2106630772 sameAs 2106630772 @default.
- W2106630772 citedByCount "43" @default.
- W2106630772 countsByYear W21066307722014 @default.
- W2106630772 countsByYear W21066307722015 @default.
- W2106630772 countsByYear W21066307722016 @default.
- W2106630772 countsByYear W21066307722017 @default.
- W2106630772 countsByYear W21066307722018 @default.
- W2106630772 countsByYear W21066307722019 @default.
- W2106630772 countsByYear W21066307722020 @default.
- W2106630772 countsByYear W21066307722021 @default.
- W2106630772 countsByYear W21066307722022 @default.
- W2106630772 crossrefType "journal-article" @default.
- W2106630772 hasAuthorship W2106630772A5045940955 @default.
- W2106630772 hasConcept C118615104 @default.
- W2106630772 hasConcept C121332964 @default.
- W2106630772 hasConcept C136119220 @default.
- W2106630772 hasConcept C185592680 @default.
- W2106630772 hasConcept C188027245 @default.
- W2106630772 hasConcept C188971069 @default.
- W2106630772 hasConcept C202444582 @default.
- W2106630772 hasConcept C24890656 @default.
- W2106630772 hasConcept C27508121 @default.
- W2106630772 hasConcept C2778023678 @default.
- W2106630772 hasConcept C2778355321 @default.
- W2106630772 hasConcept C2779057376 @default.
- W2106630772 hasConcept C33923547 @default.
- W2106630772 hasConcept C4042151 @default.
- W2106630772 hasConcept C71139939 @default.
- W2106630772 hasConcept C78023250 @default.
- W2106630772 hasConcept C78344899 @default.
- W2106630772 hasConceptScore W2106630772C118615104 @default.
- W2106630772 hasConceptScore W2106630772C121332964 @default.
- W2106630772 hasConceptScore W2106630772C136119220 @default.
- W2106630772 hasConceptScore W2106630772C185592680 @default.
- W2106630772 hasConceptScore W2106630772C188027245 @default.
- W2106630772 hasConceptScore W2106630772C188971069 @default.
- W2106630772 hasConceptScore W2106630772C202444582 @default.
- W2106630772 hasConceptScore W2106630772C24890656 @default.
- W2106630772 hasConceptScore W2106630772C27508121 @default.
- W2106630772 hasConceptScore W2106630772C2778023678 @default.
- W2106630772 hasConceptScore W2106630772C2778355321 @default.
- W2106630772 hasConceptScore W2106630772C2779057376 @default.
- W2106630772 hasConceptScore W2106630772C33923547 @default.
- W2106630772 hasConceptScore W2106630772C4042151 @default.
- W2106630772 hasConceptScore W2106630772C71139939 @default.
- W2106630772 hasConceptScore W2106630772C78023250 @default.
- W2106630772 hasConceptScore W2106630772C78344899 @default.
- W2106630772 hasIssue "3" @default.
- W2106630772 hasLocation W21066307721 @default.
- W2106630772 hasOpenAccess W2106630772 @default.
- W2106630772 hasPrimaryLocation W21066307721 @default.
- W2106630772 hasRelatedWork W1521977880 @default.
- W2106630772 hasRelatedWork W2106630772 @default.
- W2106630772 hasRelatedWork W2138971738 @default.
- W2106630772 hasRelatedWork W2371953997 @default.
- W2106630772 hasRelatedWork W2534562289 @default.
- W2106630772 hasRelatedWork W3098712411 @default.
- W2106630772 hasRelatedWork W3139146373 @default.
- W2106630772 hasRelatedWork W3189472968 @default.
- W2106630772 hasRelatedWork W4246138424 @default.
- W2106630772 hasRelatedWork W3083607220 @default.
- W2106630772 hasVolume "40" @default.
- W2106630772 isParatext "false" @default.
- W2106630772 isRetracted "false" @default.
- W2106630772 magId "2106630772" @default.
- W2106630772 workType "article" @default.