105 research outputs found
Poset products as relational models
We introduce a relational semantics based on poset products, and provide
sufficient conditions guaranteeing its soundness and completeness for various
substructural logics. We also demonstrate that our relational semantics unifies
and generalizes two semantics already appearing in the literature: Aguzzoli,
Bianchi, and Marra's temporal flow semantics for H\'ajek's basic logic, and
Lewis-Smith, Oliva, and Robinson's semantics for intuitionistic Lukasiewicz
logic. As a consequence of our general theory, we recover the soundness and
completeness results of these prior studies in a uniform fashion, and extend
them to infinitely-many other substructural logics
Neutrality and Many-Valued Logics
In this book, we consider various many-valued logics: standard, linear,
hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We
survey also results which show the tree different proof-theoretic frameworks
for many-valued logics, e.g. frameworks of the following deductive calculi:
Hilbert's style, sequent, and hypersequent. We present a general way that
allows to construct systematically analytic calculi for a large family of
non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and
p-adic valued logics characterized by a special format of semantics with an
appropriate rejection of Archimedes' axiom. These logics are built as different
extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's,
Product, and Post's logics). The informal sense of Archimedes' axiom is that
anything can be measured by a ruler. Also logical multiple-validity without
Archimedes' axiom consists in that the set of truth values is infinite and it
is not well-founded and well-ordered. On the base of non-Archimedean valued
logics, we construct non-Archimedean valued interval neutrosophic logic INL by
which we can describe neutrality phenomena.Comment: 119 page
Conjuntos construibles en modelos valuados en retÃculos
We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s
work on Intuitionistic Kripke models of Set Theory.
Firstly, we consider constructable sets within valued models of Set Theory. We present
two distinct constructions of the constructable universe: L
B and L
B
, and prove that the
they are isomorphic to V (von Neumann universe) and L (Gödel’s constructible universe),
respectively.
Secondly, we generalize Fitting’s work on Intuitionistic Kripke models of Set Theory using
Ono and Komori’s Residuated Kripke models. Based on these models, we provide a general-
ization of the von Neumann hierarchy in the context of Modal Residuated Logic and prove
a translation of formulas between it and a suited Heyting valued model. We also propose a
notion of universe of constructable sets in Modal Residuated Logic and discuss some aspects
of it.Investigamos diferentes construcciones de la teorÃa de conjuntos en Lógica Residual basados
en el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la TeorÃa de Conjuntos.
En primer lugar, consideramos conjuntos construibles dentro de modelos valuados de la
TeorÃa de Conjuntos. Presentamos dos construcciones distintas del universo construible:
L
B y L
B
, y demostramos que son isomorfos a V (universo von Neumann) y L (universo
construible de Gödel), respectivamente.
En segundo lugar, generalizamos el trabajo de Fitting sobre los modelos intuicionistas de
Kripke de la teorÃa de conjuntos utilizando los modelos residuados de Kripke de Ono y
Komori. Con base en estos modelos, proporcionamos una generalización de la jerarquÃa de
von Neumann en el contexto de la Lógica Modal Residuada y demostramos una traducción de
fórmulas entre ella y un modelo Heyting valuado adecuado. También proponemos una noción
de universo de conjuntos construibles en Lógica Modal Residuada y discutimos algunos
aspectos de la misma. (Texto tomado de la fuente)MaestrÃaMagÃster en Ciencias - MatemáticasLógica matemática, teorÃa de conjunto
- …