15 research outputs found
Toward a Dempster-Shafer theory of concepts
In this paper, we generalize the basic notions and results of Dempster-Shafer
theory from predicates to formal concepts. Results include the representation
of conceptual belief functions as inner measures of suitable probability
functions, and a Dempster-Shafer rule of combination on belief functions on
formal concepts
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
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
Game semantics for lattice-based modal {\mu}-calculus
In this paper, we generalize modal -calculus to the non-distributive
modal logic. We provide a game semantics for the developed logic. We generalize
the unfolding games on the power-set algebras to the general lattices and show
that it can be used to determine the least and the greatest fixed points of a
monotone operator on a lattice. We use this result to show the adequacy of the
game semantics. Finally, we conclude and provide some possible applications of
the non-distributive modal -calculus developed here
Labelled calculi for the logics of rough concepts
We introduce sound and complete labelled sequent calculi for the basic normal
non-distributive modal logic L and some of its axiomatic extensions, where the
labels are atomic formulas of the first order language of enriched formal
contexts, i.e., relational structures based on formal contexts which provide
complete semantics for these logics. We also extend these calculi to provide a
proof system for the logic of rough formal contexts
Algebraic proof theory for LE-logics
In this paper we extend the research programme in algebraic proof theory from
axiomatic extensions of the full Lambek calculus to logics algebraically
captured by certain varieties of normal lattice expansions (normal LE-logics).
Specifically, we generalise the residuated frames in [16] to arbitrary
signatures of normal lattice expansions (LE). Such a generalization provides a
valuable tool for proving important properties of LE-logics in full uniformity.
We prove semantic cut elimination for the display calculi D.LE associated with
the basic normal LE-logics and their axiomatic extensions with analytic
inductive axioms. We also prove the finite model property (FMP) for each such
calculus D.LE, as well as for its extensions with analytic structural rules
satisfying certain additional properties