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Inductive Inference with Procrastination: Back to Definitions
 Fundamenta Informaticae
, 1999
"... In this paper, we reconsider the denition of procrastinating learning machines. In the original denition of Freivalds and Smith [FS93], constructive ordinals are used to bound mindchanges. We investigate possibility of using arbitrary linearly ordered sets to bound mindchanges in similar way. It ..."
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In this paper, we reconsider the denition of procrastinating learning machines. In the original denition of Freivalds and Smith [FS93], constructive ordinals are used to bound mindchanges. We investigate possibility of using arbitrary linearly ordered sets to bound mindchanges in similar way. It turns out that using certain ordered sets it is possible to dene inductive inference types dierent from the previously known ones. We investigate properties of the new inductive inference types and compare them to other types. This research was supported by Latvian Science Council Grant No.93.599 and NSF Grant 9421640. Some of the results from this paper were presented earlier [AFS96]. y The third author was supported in part by NSF Grant 9301339. 1 Introduction We study inductive inference using the model developed by Gold [Gol67]. There is a well known hierarchy of larger and larger classes of learnable sets of phenomena based on the number of time a learning machine is all...
Deduction in ManyValued Logics: a Survey
 Mathware & Soft Computing, iv(2):6997
, 1997
"... this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of man ..."
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this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of manyvalued logics according to their intended application
The Mathematical Import Of Zermelo's WellOrdering Theorem
 Bull. Symbolic Logic
, 1997
"... this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs ..."
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this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his wellknown paradox, an early expression of our motif. The motif becomes fully manifest through the study of functions f :
The history and concept of computability
 in Handbook of Computability Theory
, 1999
"... We consider the informal concept of a “computable ” or “effectively calculable” function on natural numbers and two of the formalisms used to define it, computability” and “(general) recursiveness. ” We consider their origin, exact technical definition, concepts, history, how they became fixed in th ..."
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We consider the informal concept of a “computable ” or “effectively calculable” function on natural numbers and two of the formalisms used to define it, computability” and “(general) recursiveness. ” We consider their origin, exact technical definition, concepts, history, how they became fixed in their present roles, and how
SelfReplicating and SelfModifying Programs in Fraglets
"... The inherently decentralized nature of artificial chemical computing models makes them particularly attractive for building bioinspired software with selforganizing and emergent properties. Yet it is not straightforward to construct such chemical programs, either manually or automatically. We are ..."
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The inherently decentralized nature of artificial chemical computing models makes them particularly attractive for building bioinspired software with selforganizing and emergent properties. Yet it is not straightforward to construct such chemical programs, either manually or automatically. We are exploring the potential of chemical programming models for automatic programming, in the context of autonomic environments where software must operate unsupervised for unlimited periods of time. We are enhancing the Fraglets chemical language to support intrinsic genetic programming, such that programs can replicate and modify themselves during execution. The Fraglets language was originally designed to express communication protocols. We first show a few extensions towards more generic computations, then show how selfreplicating and selfmodifying programs can be created. This is a first step towards programs that can repair and optimize themselves in an autonomic way. We reveal a number of features and shortcomings of the language, suggesting fixes and future directions.
Alan Turing and the Mathematical Objection
 Minds and Machines 13(1
, 2003
"... Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet accord ..."
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Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical objection ” to his view that machines can think. Logicomathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human mathematicians presumably do. Key words: artificial intelligence, ChurchTuring thesis, computability, effective procedure, incompleteness, machine, mathematical objection, ordinal logics, Turing, undecidability The ‘skin of an onion ’ analogy is also helpful. In considering the functions of the mind or the brain we find certain operations which we can express in purely mechanical terms. This we say does not correspond to the real mind: it is a sort of skin which we must strip off if we are to find the real mind. But then in what remains, we find a further skin to be stripped off, and so on. Proceeding in this way, do we ever come to the ‘real ’ mind, or do we eventually come to the skin which has nothing in it? In the latter case, the whole mind is mechanical (Turing, 1950, p. 454–455). 1.
New foundations for imperative logic I: Logical connectives, consistency, and quantifiers
 Noûs
, 2008
"... Abstract. Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me ” is the conjunction of “kiss me ” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as th ..."
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Abstract. Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me ” is the conjunction of “kiss me ” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied⎯what more is there to say? Much more, I argue. “If you love me, kiss me”, a conditional imperative, mixes a declarative antecedent (“you love me”) with an imperative consequent (“kiss me”); it is satisfied if you love and kiss me, violated if you love but don’t kiss me, and avoided if you don’t love me. So we need a logic of threevalued imperatives which mixes declaratives with imperatives. I develop such a logic. 1.
A REVISED CONCEPT OF SAFETY FOR GENERAL ANSWER SET PROGRAMS (EXTENDED VERSION)
, 2009
"... Abstract.Some answer set solvers deal with programs with variables by requiring a safety condition on program rules. This ensures that there is a close relation between the answer sets of the program and those of its ground version. If we move beyond the syntax of disjunctive programs, for instance ..."
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Abstract.Some answer set solvers deal with programs with variables by requiring a safety condition on program rules. This ensures that there is a close relation between the answer sets of the program and those of its ground version. If we move beyond the syntax of disjunctive programs, for instance by allowing rules with nested expressions, or perhaps even arbitrary firstorder formulas, new definitions of safety are required. In this paper we consider a new concept of safety for formulas in quantified equilibrium logic where answer sets can be defined for arbitrary firstorder formulas. The new concept captures and generalises two recently proposed safety definitions: that of Lee, Lifschitz and Palla (2008) as well as that of Bria, Leone and Faber (2008). We study the main metalogical properties of safe formulas. Acknowledgements: We gratefully acknowledge support from the Spanish MEC (now MICINN) under the projects
Program equilibria and discounted computation time
 Center for
, 2008
"... Tennenholtz (GEB 2004) developed Program Equilibrium to model play in a finite twoplayer game where each player can base their strategy on the other player’s strategies. Tennenholtz’s model allowed each player to produce a “loopfree ” computer program that had access to the code for both players. H ..."
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Cited by 3 (1 self)
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Tennenholtz (GEB 2004) developed Program Equilibrium to model play in a finite twoplayer game where each player can base their strategy on the other player’s strategies. Tennenholtz’s model allowed each player to produce a “loopfree ” computer program that had access to the code for both players. He showed a folk theorem where the result of any mixedstrategy individually rational play could be an equilibrium payoff in this model even in a oneshot game. Kalai et al. gave a general folk theorem for correlated play in a more generic commitment model. We develop a new model of program equilibrium using general computational models and discounting the payoffs based on the computation time used. We give an even more general folk theorem giving correlatedstrategy payoffs down to the pure minimax of each player. We also show the existence of equilibrium in other games not covered by the earlier work. 1