This work is concerned with finite identifiability of languages from positive data. We focus on t... more This work is concerned with finite identifiability of languages from positive data. We focus on the characterization of finite identifiability [Mukouchi (1992), Lange and Zeugmann (1992)], which uses definite finite tell-tale sets (DFTTs for short), finite subsets of languages which are uniquely characteristic for them. We introduce preset learners, learning functions that explicitly use (collections of) DFTTs, and, in cases where there exist only finitely many DFTTs for each language, strict preset learners which in each case use this whole finite collection. We also introduce the concept of fastest learner, a learner which comes up with the right conjecture on any input string that objectively leaves only the right choice of language. We study the use of minimal DFTTs and their influence on the speed of finite identification. We show that: (a) in the case of finite collections of finite sets-finding a minimal DFTT is polynomial time computable, while finding a minimal-size DFTT is NP-complete; (b) in the general case-finite identifiability, minimal strict preset finite identifiability and fastest finite identifiability are shown to be mutually nonequivalent. In the end we mention the relevance of this work for dynamic epistemic logic.
On the Minimality of Definite Tell-tale Sets in Finite Identification of Languages Nina Gierasimc... more On the Minimality of Definite Tell-tale Sets in Finite Identification of Languages Nina Gierasimczuk and Dick de Jongh Institute for Logic, Language, and Computation, University of Amsterdam n. gierasimczuk@ uva. nl, dhj dejongh@ uva. nl Abstract This work is concerned with ...
Several of the presented papers contribute to the theoretical description of Georgian grammar-Asa... more Several of the presented papers contribute to the theoretical description of Georgian grammar-Asatiani on uniformities in reflexive and middle constructions, Sackokia about analytical perfects, Kikvidze and Tchantouria on honorifics and Ivanishvili and Soselia about the passive construction. Chikoidze, Dokvadze and Godabrelidze address the semantics of the verbal prefixes v (o)-and vy-in Russian. More abstract linguistic contributions are those of Shengelaia on the semantics of'empty words', Mel'cuk about'empty morphemes' and ...
Some consequences are studied of Shavrukov's theorem regarding the Magari algebras (diagonalizabl... more Some consequences are studied of Shavrukov's theorem regarding the Magari algebras (diagonalizable algebras) that are embeddable in the Magari algebra of formal arithmetical theories. Semantic characterizations of faithfully interpretable modal propositional theories in a nite number of propositional letters are given, in particular for nitely axiomatizable ones. Supported by this theory computer aided calculations on the theories of lowest complexity in one propositional letter were executed leading to a complete list of 62 formulas that axiomatize such theories under which the 8 maximal ones of particular interest.
To the standard propositional modal system of provability logic constants are added to account fo... more To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is
As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learnin... more As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learning Theory by using the tools of recursion theory \cite{Montagna97loft3}. In this paper, we present a first-order paradigm of coordination---we call this paradigm of {\em SF-coordination}. The paradigm of SF-coordination is shown to extend Montagna-Osherson's paradigm, in the sense that Montagna and Osherson's 01-agents
Journal of Pharmacology and Experimental Therapeutics, 2000
As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learnin... more As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learning Theory by using the tools of recursion theory \cite{Montagna97loft3}. In this paper, we present a first-order paradigm of coordination---we call this paradigm of {\em SF-coordination}. The paradigm of SF-coordination is shown to extend Montagna-Osherson's paradigm, in the sense that Montagna and Osherson's 01-agents
A definition is given for formulae A1, …, An in some theory T which is formalized in a propositio... more A definition is given for formulae A1, …, An in some theory T which is formalized in a propositional calculus S to be (in)dependent with respect to S. It is shown that, for intuitionistic propositional logic IPC, dependency (with respect to IPC itself) is decidable. This is an almost immediate consequence of Pitts’ uniform interpolation theorem for IPC. A reasonably simple infinite sequence of IPC-formulae Fn (p, q) is given such that IPC-formulae A and B are dependent if and only if at least on of the Fn (A, B) is provable.
This work is concerned with finite identifiability of languages from positive data. We focus on t... more This work is concerned with finite identifiability of languages from positive data. We focus on the characterization of finite identifiability [Mukouchi (1992), Lange and Zeugmann (1992)], which uses definite finite tell-tale sets (DFTTs for short), finite subsets of languages which are uniquely characteristic for them. We introduce preset learners, learning functions that explicitly use (collections of) DFTTs, and, in cases where there exist only finitely many DFTTs for each language, strict preset learners which in each case use this whole finite collection. We also introduce the concept of fastest learner, a learner which comes up with the right conjecture on any input string that objectively leaves only the right choice of language. We study the use of minimal DFTTs and their influence on the speed of finite identification. We show that: (a) in the case of finite collections of finite sets-finding a minimal DFTT is polynomial time computable, while finding a minimal-size DFTT is NP-complete; (b) in the general case-finite identifiability, minimal strict preset finite identifiability and fastest finite identifiability are shown to be mutually nonequivalent. In the end we mention the relevance of this work for dynamic epistemic logic.
On the Minimality of Definite Tell-tale Sets in Finite Identification of Languages Nina Gierasimc... more On the Minimality of Definite Tell-tale Sets in Finite Identification of Languages Nina Gierasimczuk and Dick de Jongh Institute for Logic, Language, and Computation, University of Amsterdam n. gierasimczuk@ uva. nl, dhj dejongh@ uva. nl Abstract This work is concerned with ...
Several of the presented papers contribute to the theoretical description of Georgian grammar-Asa... more Several of the presented papers contribute to the theoretical description of Georgian grammar-Asatiani on uniformities in reflexive and middle constructions, Sackokia about analytical perfects, Kikvidze and Tchantouria on honorifics and Ivanishvili and Soselia about the passive construction. Chikoidze, Dokvadze and Godabrelidze address the semantics of the verbal prefixes v (o)-and vy-in Russian. More abstract linguistic contributions are those of Shengelaia on the semantics of'empty words', Mel'cuk about'empty morphemes' and ...
Some consequences are studied of Shavrukov's theorem regarding the Magari algebras (diagonalizabl... more Some consequences are studied of Shavrukov's theorem regarding the Magari algebras (diagonalizable algebras) that are embeddable in the Magari algebra of formal arithmetical theories. Semantic characterizations of faithfully interpretable modal propositional theories in a nite number of propositional letters are given, in particular for nitely axiomatizable ones. Supported by this theory computer aided calculations on the theories of lowest complexity in one propositional letter were executed leading to a complete list of 62 formulas that axiomatize such theories under which the 8 maximal ones of particular interest.
To the standard propositional modal system of provability logic constants are added to account fo... more To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is
As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learnin... more As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learning Theory by using the tools of recursion theory \cite{Montagna97loft3}. In this paper, we present a first-order paradigm of coordination---we call this paradigm of {\em SF-coordination}. The paradigm of SF-coordination is shown to extend Montagna-Osherson's paradigm, in the sense that Montagna and Osherson's 01-agents
Journal of Pharmacology and Experimental Therapeutics, 2000
As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learnin... more As far as we know, a {\em learning to coordinate} paradigm was first introduced in Formal Learning Theory by using the tools of recursion theory \cite{Montagna97loft3}. In this paper, we present a first-order paradigm of coordination---we call this paradigm of {\em SF-coordination}. The paradigm of SF-coordination is shown to extend Montagna-Osherson's paradigm, in the sense that Montagna and Osherson's 01-agents
A definition is given for formulae A1, …, An in some theory T which is formalized in a propositio... more A definition is given for formulae A1, …, An in some theory T which is formalized in a propositional calculus S to be (in)dependent with respect to S. It is shown that, for intuitionistic propositional logic IPC, dependency (with respect to IPC itself) is decidable. This is an almost immediate consequence of Pitts’ uniform interpolation theorem for IPC. A reasonably simple infinite sequence of IPC-formulae Fn (p, q) is given such that IPC-formulae A and B are dependent if and only if at least on of the Fn (A, B) is provable.
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Papers by Dick Jongh