Normal Modal Logics in Which the Heyting Propositional Calculus can be Embedded

Kosta Došen
Additional contact information
Kosta Došen: Matematički Institut

A chapter in Mathematical Logic, 1990, pp 281-291 from Springer

Abstract: Abstract Let t(A) be the result of prefixing the necessity operator ❑ to every proper subformula, save conjunctions and disjunctions, of the formula A of the language of the Heyting propositional calculus H. It is well-known that H can be embedded by t in S4, i.e. A is provable in H iff t(A) is provable in S4. Esakia (1979), and also Blok (1976), have shown that S4Grz (defined below) is the maximal normal extension of S4 in which H can be embedded by t (as a matter of fact, we find in Esakia (1979) not t, but the translation which prefixes ❑ to every subformula; this translation is equivalent to t as far as S4 and its normal extensions are concerned).

Keywords: Modal Logic; Propositional Variable; Heyting Algebra; Normal Extension; Modal Translation (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0609-2_19

Ordering information: This item can be ordered from
http://www.springer.com/9781461306092

DOI: 10.1007/978-1-4613-0609-2_19

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().