8,509 research outputs found
An interactive semantics of logic programming
We apply to logic programming some recently emerging ideas from the field of
reduction-based communicating systems, with the aim of giving evidence of the
hidden interactions and the coordination mechanisms that rule the operational
machinery of such a programming paradigm. The semantic framework we have chosen
for presenting our results is tile logic, which has the advantage of allowing a
uniform treatment of goals and observations and of applying abstract
categorical tools for proving the results. As main contributions, we mention
the finitary presentation of abstract unification, and a concurrent and
coordinated abstract semantics consistent with the most common semantics of
logic programming. Moreover, the compositionality of the tile semantics is
guaranteed by standard results, as it reduces to check that the tile systems
associated to logic programs enjoy the tile decomposition property. An
extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory
and Practice of Logic Programmin
Nonlinear Models of Neural and Genetic Network Dynamics:\ud \ud Natural Transformations of Ćukasiewicz Logic LM-Algebras in a Ćukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations \ud
A categorical and Ćukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Ćukasiewicz Algebraic Logic models of both neural and genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable next-state/transfer functions is extended to a Ćukasiewicz Topos with an N-valued Ćukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.\u
Ćukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models
A categorical and Ćukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Ćukasiewicz Algebraic Logic models of both neural and genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Ćukasiewicz Topos with an n-valued Ćukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis
Perspectives of Neuro--Symbolic Integration -- Extended Abstract --
There is an obvious tension between symbolic and subsymbolic theories,
because both show complementary strengths and weaknesses in corresponding
applications and underlying methodologies. The resulting gap in the foundations
and the applicability of these approaches is theoretically unsatisfactory and
practically undesirable. We sketch a theory that bridges this gap between
symbolic and subsymbolic approaches by the introduction of a Topos-based
semi-symbolic level used for coding logical first-order expressions in a
homogeneous framework. This semi-symbolic level can be used for neural
learning of logical first-order theories. Besides a presentation of the general idea
of the framework, we sketch some challenges and important open problems
for future research with respect to the presented approach and the field
of neuro-symbolic integration, in general
Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models
Operational logic and bioinformatics models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes are proposed. Łukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Łukasiewicz Topos with an n-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis
Goal Translation for a Hammer for Coq (Extended Abstract)
Hammers are tools that provide general purpose automation for formal proof
assistants. Despite the gaining popularity of the more advanced versions of
type theory, there are no hammers for such systems. We present an extension of
the various hammer components to type theory: (i) a translation of a
significant part of the Coq logic into the format of automated proof systems;
(ii) a proof reconstruction mechanism based on a Ben-Yelles-type algorithm
combined with limited rewriting, congruence closure and a first-order
generalization of the left rules of Dyckhoff's system LJT.Comment: In Proceedings HaTT 2016, arXiv:1606.0542
Strongly Complete Logics for Coalgebras
Coalgebras for a functor model different types of transition systems in a
uniform way. This paper focuses on a uniform account of finitary logics for
set-based coalgebras. In particular, a general construction of a logic from an
arbitrary set-functor is given and proven to be strongly complete under
additional assumptions. We proceed in three parts. Part I argues that sifted
colimit preserving functors are those functors that preserve universal
algebraic structure. Our main theorem here states that a functor preserves
sifted colimits if and only if it has a finitary presentation by operations and
equations. Moreover, the presentation of the category of algebras for the
functor is obtained compositionally from the presentations of the underlying
category and of the functor. Part II investigates algebras for a functor over
ind-completions and extends the theorem of J{\'o}nsson and Tarski on canonical
extensions of Boolean algebras with operators to this setting. Part III shows,
based on Part I, how to associate a finitary logic to any finite-sets
preserving functor T. Based on Part II we prove the logic to be strongly
complete under a reasonable condition on T
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