1,720,969 research outputs found
Computing Uniform Interpolants in Nilpotent Minimum Logic
No full textIn this note we exploit a combinatorial characterization of free finitely generated Nilpotent Minimum algebras, to give a constructive proof of the uniform interpolation property for Nilpotent Minimum logic. This method allows us to explicitly compute strongest uniform interpolants in Nilpotent Minimum logic
Poset representation for free RDP-algebras
No full textIn this paper we give a combinatorial characterization of truth functions associated with RDP logic, following analogous results obtained for Godel logic
Finite RDP-algebras : duality, coproducts and logic
No full textThe variety of RDP-algebras forms the algebraic semantics of RDP-logic, the many-valued propositional logic of the revised drastic product left-continuous triangular norm and its residual. We prove a Priestley duality for finite RDP-algebras, and obtain an explicit description of co-
products of finite RDP-algebras. In this light, we give a combinatorial representation of free finitely generated RDP-algebras, which we exploit to construct normal forms, strongest deductive interpolants, and most general unifiers. We prove that RDP-unification is unitary, and that the tautology problem for RDP-logic is coNP-complete
DUALITIES AND REPRESENTATIONS FOR MANY-VALUED LOGICS IN THE HIERARCHY OF WEAK NILPOTENT MINIMUM.
Full text linkIn this thesis we study particular subclasses of WNM algebras.
The variety of WNM algebras forms the algebraic semantics of the
WNM logic, a propositional many-valued logic that generalizes some
well-known case in the setting of triangular norms logics.
WNM logic lies in the hierarchy of schematic extensions of MTL, which is
proven to be the logic of all left-continuous triangular norms and their residua.
In this work, I have extensively studied two extensions
of WNM logic, namely RDP logic and NMG logic, from the point of view of
algebraic and categorical logic.
We develop spectral dualities between the varieties of algebras
corresponding to RDP logic and NMG logic, and suitable defined combinatorial categories.
Categorical dualities allow to give algorithmic construction of products in
the dual categories obtaining computable descriptions of coproducts
(which are notoriously hard to compute working only in the algebraic side)
for the corresponding finite algebras. As a byproduct, representation theorems
for finite algebras and free finitely generated algebras in the considered varieties
are obtained. This latter characterization is especially useful to provide explicit
construction of a number of objects relevant from the point of view of the logical
interpretation of the varieties of algebras: normal forms, strongest deductive
interpolants and most general unifiers
Valuations in Nilpotent Minimum Logic
No full textThe Euler characteristic can be defined as a special kind of valuation on finite distributive lattices. This work begins with some brief consideration on the role of the Euler characteristic on NM algebras, the algebraic counterpart of Nilpotent Minimum logic. Then, we introduce a new valuation, a modified version of the Euler characteristic we call idempotent Euler characteristic. We show that the new valuation encodes information about the formulas in NM propositional logic
Free weak nilpotent minimum algebras
No full textWe give a combinatorial description of the finitely generated free weak nilpotent minimum algebras and provide explicit constructions of normal forms.© 2016, Springer-Verlag Berlin Heidelberg.The second author is supported by the FWF Austrian Science Fund (Parameterized Compilation, P26200). The third author is supported by a Marie Curie INdAM-COFUND Outgoing Fellowship.Peer Reviewe
On gödel algebras of concepts
No full textBeside algebraic and proof-theoretical studies, a number of different approaches have been pursued in order to provide a complete intuitive semantics for many-valued logics. Our intention is to use the powerful tools offered by formal concept analysis (FCA) to obtain further intuition about the intended semantics of a prominent many-valued logic, namely Gödel, or Gödel-Dummett, logic. In this work, we take a first step in this direction. Gödel logic seems particularly suited to the approach we aim to follow, thanks to the properties of its corresponding algebraic variety, the class of Gödel algebras. Furthermore, Gödel algebras are prelinear Heyting algebras. This makes Gödel logic an ideal contact-point between intuitionistic and many-valued logics. In the literature one can find several studies on relations between FCA and fuzzy logics. These approaches often amount to equipping both intent and extent of concepts with connectives taken by some many-valued logic. Our approach is different. Since Gödel algebras are (residuated) lattices, we want to understand which type of concepts are expressed by these lattices. To this end, we investigate the concept lattice of the standard context obtained from the lattice reduct of a Gödel algebra. We provide a characterization of Gödel implication between concepts, and of the Gödel negation of a concept. Further, we characterize a Gödel algebra of concepts. Some concluding remarks will show how to associate (equivalence classes of) formulæ of Gödel logic with their corresponding formal concepts
Computing Duals of Finite Gödel Algebras
Full text linkWe introduce an algorithm that computes and counts the duals of finite Gödel-Dummett algebras of k≥1 elements. The computational cost of our algorithm depends on the factorization of k, nevertheless a Python implementation is sufficiently fast to compute the results for very large values of k
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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