Monographs in Theoretical Computer Science An EATCS Series, 2002
Semantic structures of the logics presented in this chapter contain relations that are the counte... more Semantic structures of the logics presented in this chapter contain relations that are the counterparts to indiscernibility relations derived from information systems. The modal operators of the logics represent approximation operators. In Sect. 8.2 we introduce the logic DALLA and we present its Hilbert-style deductive system. A specific property of the semantic structures of DALLA is that any two relations in these structures satisfy a condition referred to as local agreement of the relations. This condition is equivalent to the property that the union of equivalence relations is also an equivalence relation. The language of DALLA includes operators acting on indiscernibility relations, namely intersection and transitive closure of relations. Consequently, we can represent in this logic the corresponding approximation operators and relationships among them. In Sect. 8.3 we study a family of logics for reasoning about relative indiscernibility relations. In Sect. 8.4 we introduce the class of LA-logics that generalises DALLA-style logics by assuming various classes of local agreements in the semantic structures of these logics. We present a Hilbert-style deductive system for LA-logics equipped with a finite amount of constraints on local agreement of relations. In Sect. 8.5 we show that the class of LA-logics is broad enough to capture some fuzzy logics also.
International audienceThe purpose of this paper is to elaborate a formal framework for expressing... more International audienceThe purpose of this paper is to elaborate a formal framework for expressing and proving informational representability of abstract frames. The property of informational representability can be meaningful in investigations of nonclassical logics.We introduce a general notion of informational representability, we develop a method of proving informationalrepresentability and we give examples of informational representability and non-representability of frames
The aim of this note is to characterize those doubly ordered frames $\langle X, \leq_1, \leq_2 \r... more The aim of this note is to characterize those doubly ordered frames $\langle X, \leq_1, \leq_2 \rangle$ which are embeddable into the canonical frame of its Urquhart complex algebra.
Monographs in Theoretical Computer Science An EATCS Series, 2002
Semantic structures of the logics presented in this chapter contain relations that are the counte... more Semantic structures of the logics presented in this chapter contain relations that are the counterparts to indiscernibility relations derived from information systems. The modal operators of the logics represent approximation operators. In Sect. 8.2 we introduce the logic DALLA and we present its Hilbert-style deductive system. A specific property of the semantic structures of DALLA is that any two relations in these structures satisfy a condition referred to as local agreement of the relations. This condition is equivalent to the property that the union of equivalence relations is also an equivalence relation. The language of DALLA includes operators acting on indiscernibility relations, namely intersection and transitive closure of relations. Consequently, we can represent in this logic the corresponding approximation operators and relationships among them. In Sect. 8.3 we study a family of logics for reasoning about relative indiscernibility relations. In Sect. 8.4 we introduce the class of LA-logics that generalises DALLA-style logics by assuming various classes of local agreements in the semantic structures of these logics. We present a Hilbert-style deductive system for LA-logics equipped with a finite amount of constraints on local agreement of relations. In Sect. 8.5 we show that the class of LA-logics is broad enough to capture some fuzzy logics also.
International audienceThe purpose of this paper is to elaborate a formal framework for expressing... more International audienceThe purpose of this paper is to elaborate a formal framework for expressing and proving informational representability of abstract frames. The property of informational representability can be meaningful in investigations of nonclassical logics.We introduce a general notion of informational representability, we develop a method of proving informationalrepresentability and we give examples of informational representability and non-representability of frames
The aim of this note is to characterize those doubly ordered frames $\langle X, \leq_1, \leq_2 \r... more The aim of this note is to characterize those doubly ordered frames $\langle X, \leq_1, \leq_2 \rangle$ which are embeddable into the canonical frame of its Urquhart complex algebra.
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