21,660 research outputs found
Logics for Rough Concept Analysis
Taking an algebraic perspective on the basic structures of Rough Concept
Analysis as the starting point, in this paper we introduce some varieties of
lattices expanded with normal modal operators which can be regarded as the
natural rough algebra counterparts of certain subclasses of rough formal
contexts, and introduce proper display calculi for the logics associated with
these varieties which are sound, complete, conservative and with uniform cut
elimination and subformula property. These calculi modularly extend the
multi-type calculi for rough algebras to a `nondistributive' (i.e. general
lattice-based) setting
Logics for Rough Concept Analysis
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough algebra counterparts of certain subclasses of rough formal contexts, and introduce proper display calculi for the logics associated with these varieties which are sound, complete, conservative and with uniform cut elimination and subformula property. These calculi modularly extend the multi-type calculi for rough algebras to a ‘nondistributive’ (i.e. general lattice-based) setting.https://digitalcommons.chapman.edu/scs_books/1060/thumbnail.jp
Two-sorted Modal Logic for Formal and Rough Concepts
In this paper, we propose two-sorted modal logics for the representation and
reasoning of concepts arising from rough set theory (RST) and formal concept
analysis (FCA). These logics are interpreted in two-sorted bidirectional
frames, which are essentially formal contexts with converse relations. On one
hand, the logic contains ordinary necessity and possibility
modalities and can represent rough set-based concepts. On the other hand, the
logic has window modality that can represent formal concepts. We
study the relationship between \textbf{KB} and \textbf{KF} by proving a
correspondence theorem. It is then shown that, using the formulae with modal
operators in \textbf{KB} and \textbf{KF}, we can capture formal concepts based
on RST and FCA and their lattice structures
Understanding Predication in Conceptual Spaces
We argue that a cognitive semantics has to take into account the possibly
partial information that a cognitive agent has of the world. After discussing
Gärdenfors's view of objects in conceptual spaces, we offer a number of viable
treatments of partiality of information and we formalize them by means of alternative
predicative logics. Our analysis shows that understanding the nature of simple
predicative sentences is crucial for a cognitive semantics
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