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Some philosophical problems from the standpoint of artificial intelligence
 AI, IN MACHINE INTELLIGENCE 4, MELTZER AND MICHIE (EDS
, 1969
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On the size of weights for threshold gates
 SIAM Journal on Discrete Mathematics
, 1994
"... We provethatifn is a power of 2 then there is a threshold function that on n inputs that requires weights of size around 2 (n log n)=2;n. This almost matches the known upper bounds. ..."
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Cited by 55 (0 self)
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We provethatifn is a power of 2 then there is a threshold function that on n inputs that requires weights of size around 2 (n log n)=2;n. This almost matches the known upper bounds.
A Taxonomy of Csystems
, 2002
"... The logics of formal inconsistency (LFIs) are paraconsistent logics which permit us to internalize the concepts of consistency or inconsistency inside our object language, introducing new operators to talk about them, and allowing us, in principle, to logically separate the notions of contradictorin ..."
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Cited by 41 (15 self)
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The logics of formal inconsistency (LFIs) are paraconsistent logics which permit us to internalize the concepts of consistency or inconsistency inside our object language, introducing new operators to talk about them, and allowing us, in principle, to logically separate the notions of contradictoriness and of inconsistency. We present the formal definitions of these logics in the context of General Abstract Logics, argue that they in fact represent the majority of all paraconsistent logics existing up to this point, if not the most exceptional ones, and we single out a subclass of them called Csystems, as the LFIs that are built over the positive basis of some given consistent logic. Given precise characterizations of some received logical principles, we point out that the gist of paraconsistent logic lies in the Principle of Explosion, rather than in the Principle of NonContradiction, and we also sharply distinguish these two from the Principle of NonTriviality, considering the next various weaker formulations of explosion, and investigating their interrelations. Subsequently, we present the syntactical formulations of some of the main Csystems based on classical logic, showing how several wellknown logics in the literature can be recast as such a kind of Csystems, and carefully study their properties and shortcomings, showing for instance how they can be used to faithfully
The Origin of Relation Algebras in the Development and Axiomatization of the Calculus of Relations
, 1991
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On Strongest Necessary and Weakest Sufficient
 Artificial Intelligence
, 2000
"... Given a propositional theory T and a proposition q, a sufficient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T . In this paper, we propose a notion of strongest necessary and weakest sufficient conditions. ..."
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Cited by 27 (1 self)
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Given a propositional theory T and a proposition q, a sufficient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T . In this paper, we propose a notion of strongest necessary and weakest sufficient conditions. Intuitively, the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory, and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory. We show that these two conditions are dual ones, and can be naturally extended to arbitrary formulas. We investigate some computational properties of these two conditions and discuss some of their potential applications.
A Capacitive ThresholdLogic Gate
, 1996
"... A dense and fast thresholdlogic gate with a very high fanin capacity is described. The gate performs sumofproduct and thresholding operations in an architecture comprising a polytopoly capacitor array and an inverter chain. The Boolean function performed by the gate is soft programmable. This i ..."
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Cited by 26 (2 self)
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A dense and fast thresholdlogic gate with a very high fanin capacity is described. The gate performs sumofproduct and thresholding operations in an architecture comprising a polytopoly capacitor array and an inverter chain. The Boolean function performed by the gate is soft programmable. This is accomplished by adjusting the threshold with a dc voltage. Essentially, the operation is dynamic and thus, requires periodic reset. However, the gate can evaluate multiple input vectors in between two successive reset phases because evaluation is nondestructive. Asynchronous operation is, therefore, possible. The paper presents an electrical analysis of the gate, identifies its limitations, and describes a test chip containing four different gates of fanin 30, 62, 127, and 255. Experimental results confirming proper functionality in all these gates are given, and applications in arithmetic and logic function blocks are described. I. INTRODUCTION T HRESHOLD logic (TL) originally emerged ...
What is an Inference Rule?
 Journal of Symbolic Logic
, 1992
"... What is an inference rule? This question does not have a unique answer. One usually nds two distinct standard answers in the literature: validity inference ( ` v ' if for every substitution , the validity of [] entails the validity of [']), and truth inference ( ` t ' if for every substitution , ..."
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Cited by 19 (2 self)
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What is an inference rule? This question does not have a unique answer. One usually nds two distinct standard answers in the literature: validity inference ( ` v ' if for every substitution , the validity of [] entails the validity of [']), and truth inference ( ` t ' if for every substitution , the truth of [] entails the truth of [']). In this paper we introduce a general semantic framework that allows us to investigate the notion of inference more carefully. Validity inference and truth inference are in some sense the extremal points in our framework. We investigate the relationship between various types of inference in our general framework, and consider the complexity of deciding if an inference rule is sound, in the context of a number of logics of interest: classical propositional logic, a nonstandard propositional logic, various propositional modal logics, and rstorder logic.
Bounded Independence Fools Halfspaces
 In Proc. 50th Annual Symposium on Foundations of Computer Science (FOCS), 2009
"... We show that any distribution on {−1, +1} n that is kwise independent fools any halfspace (a.k.a. linear threshold function) h: {−1, +1} n → {−1, +1}, i.e., any function of the form h(x) = sign ( ∑n i=1 wixi − θ) where the w1,..., wn, θ are arbitrary real numbers, with error ɛ for k = O(ɛ−2 log 2 ..."
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Cited by 19 (8 self)
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We show that any distribution on {−1, +1} n that is kwise independent fools any halfspace (a.k.a. linear threshold function) h: {−1, +1} n → {−1, +1}, i.e., any function of the form h(x) = sign ( ∑n i=1 wixi − θ) where the w1,..., wn, θ are arbitrary real numbers, with error ɛ for k = O(ɛ−2 log 2 (1/ɛ)). Our result is tight up to log(1/ɛ) factors. Using standard constructions of kwise independent distributions, we obtain the first explicit pseudorandom generators G: {−1, +1} s → {−1, +1} n that fool halfspaces. Specifically, we fool halfspaces with error ɛ and seed length s = k · log n = O(log n · ɛ−2 log 2 (1/ɛ)). Our approach combines classical tools from real approximation theory with structural results on halfspaces by Servedio (Comput. Complexity 2007).
Hybridizing Concept Languages
 Annals of Mathematics and Artificial Intelligence
"... This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the wellknown correspondences between modal and description logics, two hybrid languages are dened. These languages are called `hybrid' because, as well as the familiar prop ..."
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Cited by 17 (8 self)
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This paper shows how to increase the expressivity of concept languages using a strategy called hybridization. Building on the wellknown correspondences between modal and description logics, two hybrid languages are dened. These languages are called `hybrid' because, as well as the familiar propositional variables and modal operators, they also contain variables across individuals and a binder that binds these variables. As is shown, combining aspects of modal and rstorder logic in this manner allows the expressivity of concept languages to be boosted in a natural way, making it possible to dene number restrictions, collections of individuals, irreexivity of roles, and TBox and ABoxstatements. Subsequent addition of the universal modality allows the notion of subsumption to internalized, and enables the representation of queries to arbitrary rstorder knowledge bases. The paper notes themes shared by the hybrid and concept language literatures, and draws attention t...