A Modal Characterization of Indiscernibility and Similarity Relations in Pawlak's Information Systems

@inproceedings{Vakarelov2005AMC,
  title={A Modal Characterization of Indiscernibility and Similarity Relations in Pawlak's Information Systems},
  author={Dimiter Vakarelov},
  booktitle={RSFDGrC},
  year={2005}
}
  • D. Vakarelov
  • Published in RSFDGrC 31 August 2005
  • Computer Science
In this paper we present a modal logic IND for Pawlak's information systems giving a modal characterization of 9 informational relations: strong indiscernibility, as well as weak and strong versions of forward and backward informational inclusion, as well as positive and negative similarities. IND extends the logic INF introduced in [4] by adding a modality corresponding to strong indiscernibility relation. The main problem in the modal treating of strong indiscernibility is that its definition… 
Modal logics for mereotopological relations
TLDR
It is shown that MTML possesses fmp with respect to a class of non-st andard models, which implies its decidability, and is proposed also a solu- tion of the main open problem, formulated in (17), to find a decidable modal logic for topological relations.
Intransitive Linear Temporal Logic, Knowledge from Past, Decidability, Admissible Rules
TLDR
The notion of knowledge might be represented in linear temporal logic based at a conception of intransitive time with uniform intransitivity to solve the problem of admissibility for inference rules.
Intransitive Temporal Multi-agent's Logic, Knowledge and Uncertainty, Plausibility
TLDR
This work studies intransitive temporal logic implementing multiagent’s approach and formalizing knowledge and uncertainty and considers a modification of this logic - temporal logic with uniform non-transitivity and solve problem of recognizing admissibility in this logic.
Nontransitive temporal multiagent logic, information and knowledge, deciding algorithms
TLDR
The main results are the algorithms that compute satisfiability and solve decidability (and so provide solutions to these problems) that are based on nontransitive linear time.
Non-transitive linear temporal logic and logical knowledge operations
TLDR
The main result of Section 5 is a solution of the decidability problem for LTLNT, and the decision algorithm is found and described in details and uniform bound (m) for non-transitivity is introduced.
Logic on Similarity Based Rough Sets
TLDR
The author shows that there is a logical system relying on similarity base sets in which the truth values of first-order formulas can be counted in an effective simple way.
Linear Non-Transitive Temporal Logic, Knowledge Operations, Algorithms for Admissibility
TLDR
Algorithms are found solving problems of satisfiability, decidability and admissibility of inference rules, conceptions of knowledge and agent's knowledge in non-transitive temporal linear logic LTL(Past,m).
A Note on Parameterised Knowledge Operations in Temporal Logic
TLDR
This paper models knowledge in terms of linear temporal logic with {\em past}.
Approximation of Sets Based on Partial Covering
TLDR
A general set theoretic approximation framework is defined and which conditions have to be satisfied by the upper and lower $\mathfrak{B}$ -approximations so that they form a (regular) Galois connection.
...
...

References

SHOWING 1-6 OF 6 REFERENCES
Information Systems, Similarity Relations and Modal Logics
TLDR
The completeness theorems for the introduced modal logics with respect to their standard semantics are introduced and their “query meaning” is discussed.
A duality between Pawlak's knowledge representation systems and bi-consequence systems
TLDR
It is shown that INF possesses finite model property and hence is decidable and a completeness theorem for the corresponding modal logic INF is proved.
Incomplete Information: Structure, Inference, Complexity
  • S. Demri, E. Orlowska
  • Computer Science
    Monographs in Theoretical Computer Science An EATCS Series
  • 2002
TLDR
1. Mathematical Prerequisites for Information Logics: Structures with Incomplete Information, Representability and Duality, and Informational Representability.
Incomplete Information: Rough Set Analysis
TLDR
This book discusses Rough Sets, Rough Set-Based Deduction Methods, and Similarity-Based Reasoning, a Logic for Reasoning about Similarity Information Systems, Similarity Relations and Modal Logics.
Representation of Nondeterministic Information
Modal Logic