Name
Abstract | ||
|---|---|---|
With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$ , providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is admissible. We prove that any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s00153-011-0250-y | Arch. Math. Log. |
Keywords | Field | DocType |
latter rule,admissible rule,extended rule,algebraizable logic,structural finitary consequence operator,variable p,intermediate logic,disjunction property,lor p,latter condition,structural inference rule | Discrete mathematics,Combinatorics,Quasivariety,Heyting algebra,Finitary,Admissible rule,Operator (computer programming),If and only if,Rule of inference,Mathematics,Intermediate logic | Journal |
Volume | Issue | ISSN |
51 | 1-2 | 1432-0665 |
Citations | PageRank | References |
6 | 0.50 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander Citkin | 1 | 7 | 0.91 |