Theoretical Computer Science
Modal logics for knowledge representation systems
Theoretical Computer Science
On relationship between modified sets, topological spaces and rough sets
Fuzzy Sets and Systems
Applying modifiers to knowledge acquisition
Information Sciences—Informatics and Computer Science: An International Journal - Special issue computing with words
Modal logic
Incomplete Information: Structure, Inference, Complexity
Incomplete Information: Structure, Inference, Complexity
Display Calculi for Logics with Relative Accessibility Relations
Journal of Logic, Language and Information
On the structure of rough approximations
Fundamenta Informaticae
Mathematical Structures in Computer Science
Computational Complexity of Multimodal Logics Based on Rough Sets
Fundamenta Informaticae
Modal-Like Operators in Boolean Lattices, Galois Connections and Fixed Points
Fundamenta Informaticae
A unifying study between modal-like operators, topologies and fuzzy sets
Fuzzy Sets and Systems
On the structure of generalized rough sets
Information Sciences: an International Journal
Optimal triangular decompositions of matrices with entries from residuated lattices
International Journal of Approximate Reasoning
Algebraic aspects of generalized approximation spaces
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
On galois connections and soft computing
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advences in computational intelligence - Volume Part II
International Journal of Approximate Reasoning
Duality, conjugacy and adjointness of approximation operators in covering-based rough sets
International Journal of Approximate Reasoning
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In this paper, Information Logic of Galois Connections (ILGC) suited for approximate reasoning about knowledge is introduced. In addition to the three classical propositional logic axioms and the inference rule of modus ponens, ILGC contains only two auxiliary rules of inference mimicking the performance of Galois connections of lattice theory, and this makes ILGC comfortable to use due to the flip-flop property of the modal connectives. Kripke-style semantics based on information relations is defined for ILGC. It is also shown that ILGC is equivalent to the minimal tense logic K"t, and decidability and completeness of ILGC follow from this observation. Additionally, relationship of ILGC to the so-called classical modal logics is studied. Namely, a certain composition of Galois connection mappings forms a lattice-theoretical interior operator, and this motivates us to axiomatize a logic of these compositions. It turns out that this logic satisfies the axioms of the non-normal logic EMT4. Hence, EMT4 can be viewed to be embedded in ILGC. EMT4 is complete with respect to the neighbourhood semantics. Here, we introduce an alternative semantics for EMT4. This is done by defining the so-called interior models, and completeness of EMT4 is proved with respect to the interior semantics.