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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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Why is modal logic so robustly decidable?
 OF DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, AMERICAN MATHEMATICAL SOCIETY
, 1996
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On the size of weights for threshold gates
 SIAM JOURNAL ON DISCRETE MATHEMATICS
, 1994
"... We prove that if n 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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We prove that if n 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
 PARACONSISTENCY: THE LOGICAL WAY TO THE INCONSISTENT
, 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 58 (19 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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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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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).
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 38 (2 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.