A Syntactic Approach to Unification in Transitive Reflexive Modal Logics

@article{Iemhoff2016ASA,
  title={A Syntactic Approach to Unification in Transitive Reflexive Modal Logics},
  author={Rosalie Iemhoff},
  journal={Notre Dame J. Formal Log.},
  year={2016},
  volume={57},
  pages={233-247}
}
This paper contains a proof-theoretic account of unification in transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible. New proofs of theorems on unification types are presented and these results are extended to negationless fragments. In particular, a syntactic proof of Ghilardi’s result that S4 has finitary unification is provided. In this approach the relation between classical valuations, projective unifiers and admissible… 
View via Publisher
projecteuclid.org
6 Citations
Background Citations
3

6 Citations

Citation Type

Citation Type

About the unification types of the modal logics determined by classes of deterministic frames
TLDR
The unification types of some modal logics determined by classes of deterministic frames are studied, finding that they are either infinitary, finitary, or unitary, depending on the cardinality of its minimal complete sets of unifiers.
UNIFICATION IN INTERMEDIATE LOGICS
TLDR
It is shown that many existing results can be extended to fragments that at least contain implication and conjunction, and it is shown how from the closure of a formula under the Visser rules a proof of the formula under a projective unifier can be obtained.
Unification in Pretabular Extensions of S4
TLDR
It is shown that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification, and complete sets of unifiers in logics are described.
Unification with parameters in the implication fragment of classical propositional logic
In this paper, we show that the implication fragment of classical propositional logic is finitary for unification with parameters.
Almost structural completeness; an algebraic approach
Finitary unification in locally tabular modal logics characterized

References

SHOWING 1-10 OF 35 REFERENCES
Unification in fragments of intermediate logics
This paper contains a proof theoretic treatment of some aspects of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain…
Admissible rules in the implication-negation fragment of intuitionistic logic
Unification in modal and description logics
TLDR
A survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics is given.
Projective unification in modal logic
TLDR
It is shown that every unifiable formula has a projective unifier in L iff L contains S4.3, and that all normal modal logics L containing S 4.3 are almost structurally complete, i.e. all (structural) admissible rules having unifiable premises are derivable in L.
Hypersequent Systems for the Admissible Rules of Modal and Intermediate Logics
TLDR
This paper extends a proof-theoretic framework to cover derivability of the admissible rules of intermediate logics and a wider class of modal logics, in this case by taking hypersequent rules as the basic objects.
Proof theory for admissible rules
Unification in Intuitionistic Logic
We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having…
Admissible Rules of Modal Logics
We construct explicit bases of admissible rules for a representative class of normal modal logics (including the systems K4, GL, S4, Grz, and GL:3), by extending the methods of S. Ghilardi and R.…
On the admissible rules of intuitionistic propositional logic
TLDR
A conjecture by de Jongh and Visser is proved and a proof system for the admissible rules of intuitionistic propositional logic is presented and semantic criteria for admissibility are given.
Admissibility of Logical Inference Rules
...
...