6,850 research outputs found
On the existence of free models in fuzzy universal Horn classes
This paper is a contribution to the study of the universal Horn fragment of predicate fuzzy logics, focusing on some relevant notions in logic programming. We introduce the notion of term structure associated to a set of formulas in the fuzzy context and we show the existence of free models in fuzzy universal Horn classes. We prove that every equality-free consistent universal Horn fuzzy theory has a Herbrand model
Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic
This paper is a contribution to graded model theory, in the context of
mathematical fuzzy logic. We study characterizations of classes of graded
structures in terms of the syntactic form of their first-order axiomatization.
We focus on classes given by universal and universal-existential sentences. In
particular, we prove two amalgamation results using the technique of diagrams
in the setting of structures valued on a finite MTL-algebra, from which
analogues of the Los--Tarski and the Chang--Los--Suszko preservation theorems
follow
Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces
We present a generalisation of the theory of quantitative algebras of
Mardare, Panangaden and Plotkin where (i) the carriers of quantitative algebras
are not restricted to be metric spaces and can be arbitrary fuzzy relations or
generalised metric spaces, and (ii) the interpretations of the algebraic
operations are not required to be nonexpansive. Our main results include: a
novel sound and complete proof system, the proof that free quantitative
algebras always exist, the proof of strict monadicity of the induced
Free-Forgetful adjunction, the result that all monads (on fuzzy relations) that
lift finitary monads (on sets) admit a quantitative equational presentation.Comment: Appendix remove
Special issue on logics and artificial intelligence
There is a significant range of ongoing challenges in artificial intelligence (AI) dealing with reasoning, planning, learning, perception and cognition, among others. In this scenario, many-valued logics emerge as one of the topics in many of the solutions to some of those AI problems. This special issue presents a brief introduction to the relation between logics and AI and collects recent research works on logic-based approaches in AI
Admissibility via Natural Dualities
It is shown that admissible clauses and quasi-identities of quasivarieties
generated by a single finite algebra, or equivalently, the quasiequational and
universal theories of their free algebras on countably infinitely many
generators, may be characterized using natural dualities. In particular,
axiomatizations are obtained for the admissible clauses and quasi-identities of
bounded distributive lattices, Stone algebras, Kleene algebras and lattices,
and De Morgan algebras and lattices.Comment: 22 pages; 3 figure
A Semantic Framework for Neural-Symbolic Computing
Two approaches to AI, neural networks and symbolic systems, have been proven
very successful for an array of AI problems. However, neither has been able to
achieve the general reasoning ability required for human-like intelligence. It
has been argued that this is due to inherent weaknesses in each approach.
Luckily, these weaknesses appear to be complementary, with symbolic systems
being adept at the kinds of things neural networks have trouble with and
vice-versa. The field of neural-symbolic AI attempts to exploit this asymmetry
by combining neural networks and symbolic AI into integrated systems. Often
this has been done by encoding symbolic knowledge into neural networks.
Unfortunately, although many different methods for this have been proposed,
there is no common definition of an encoding to compare them. We seek to
rectify this problem by introducing a semantic framework for neural-symbolic
AI, which is then shown to be general enough to account for a large family of
neural-symbolic systems. We provide a number of examples and proofs of the
application of the framework to the neural encoding of various forms of
knowledge representation and neural network. These, at first sight disparate
approaches, are all shown to fall within the framework's formal definition of
what we call semantic encoding for neural-symbolic AI
From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
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