# Independent Bases of Admissible Rules

@article{Jebek2008IndependentBO, title={Independent Bases of Admissible Rules}, author={Emil Jeř{\'a}bek}, journal={Log. J. IGPL}, year={2008}, volume={16}, pages={249-267} }

We show that IPC , K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules.

## 35 Citations

### Admissible Bases Via Stable Canonical Rules

- MathematicsStud Logica
- 2016

AbstractWe establish the dichotomy property for stable canonical multi-conclusion
rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for…

### On Rules

- PhilosophyJ. Philos. Log.
- 2015

This paper contains a brief overview of the area of admissible rules with an emphasis on results about intermediate and modal propositional logics. No proofs are given but many references to the…

### UvA-DARE ( Digital Academic Repository ) Admissible bases via stable canonical rules

- Mathematics
- 2015

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these…

### The complexity of admissible rules of Łukasiewicz logic

- MathematicsJ. Log. Comput.
- 2013

This work investigates the computational complexity of admissibility of inference rules in infinite-valued Łukasiewicz propositional logic and establishes that admissible rules of Ł are PSPACE-complete.

### Multiple Conclusion Rules in Logics with the Disjunction Property

- PhilosophyLFCS
- 2016

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of…

### Unification in modal and description logics

- Philosophy, Computer ScienceLog. J. IGPL
- 2011

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.

### Linear Temporal Logic LTL: Basis for Admissible Rules

- Philosophy, MathematicsJ. Log. Comput.
- 2011

The current article aims to provide an explicit (infinite) basis for rules admissible in LTL with operations Until and Next and to suggest a recursive infinite basis for admissible rules.

### Intuitionistic Rules : Admissible Rules of Intermediate Logics

- Computer Science
- 2015

It is proved that finite models can not provide sound and complete semantics for logics of width greater than two that admit one particular variant of the Visser rules.

### Canonical rules

- MathematicsThe Journal of Symbolic Logic
- 2009

Abstract We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the…

### Reasoning and Inference Rules in Basic Linear Temporal Logic BLTL\mathcal{BLTL}

- Computer ScienceKES
- 2010

Main result is found explicit basis for rules admissible in BLTL (which, in particular, allows to compute admissible rules).

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