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Trial and error predicates and the solution to a problem of Mostowski

Hilary Putnam
1965 Journal of Symbolic Logic (JSL)  
The machine then "prints out" a finite sequence of "yesses" and "nos".  ...  The purpose of this paper is to present two groups of results which have turned out to have a surprisingly close interconnection.  ...  In other words Question 1: What are necessary and sufficient conditions (in terms of the Kleene-Mostowski Hierarchy of arithmetical predicates) that P be a trial and error predicate?  ... 
doi:10.2307/2270581 fatcat:44rldnefazdjfdmm73mhbsylxi

Page 666 of Mathematical Reviews Vol. 33, Issue 4 [page]

1967 Mathematical Reviews  
Putnam, Hilary 3923 Trial and error predicates and the solution to a problem of Mostowski. J. Symbolic Logic 30 (1965), 49-57.  ...  The author first poses the problem of defining the trial and error and k-trial predicates in terms of the arithmetical hierarchy.  ... 

JSL volume 30 issue 4 Cover and Back matter

1965 Journal of Symbolic Logic (JSL)  
Trial and error predicates and the solution to a problem of Mostowski. An algebraic study of Diodorean modal systems. By R. A. BULL . . 58 On the logic of incomplete answers. By M. J.  ...  By GUSTAV HENSEL and HILARY PUTNAM 69 Reviews 87 Notice of a meeting of the Association for Symbolic Logic 112 Venn-type diagrams for arguments of n terms. By DANIEL E. ANDER-SON and FRANK L.  ... 
doi:10.1017/s0022481200055845 fatcat:bxhbwrkfrrfsdfmdd7lrvqzth4

JSL volume 30 issue 1 Cover and Front matter

1965 Journal of Symbolic Logic (JSL)  
. > 28 Trial and error predicates and the solution to a problem of Mostowski, By " HILARY PUTNAM. . . " .- - ^, . -, . , " , . . 49 ' Aa algebraic study-of Diodprean modal systems. By R. A.  ...  be typed with wide margin and wide spacing (preferably On a separate sheet) ^ If an article is of more than thirty two (printed) pages is length, the editors reserve the right to dividjs it between two  ... 
doi:10.1017/s0022481200057054 fatcat:cq6vhmsp7ffmnjyk4wnbt6jpmi

The Kleene Hierarchy Classification of Recursively Random Sequences

D. W. Loveland
1966 Transactions of the American Mathematical Society  
We confine our attention to sequences of O's and l's and then make the natural correspondence between sequences and sets by associating with the infinite sequence a0, alt a2,... the set {/1 a¡= 1}.  ...  In essence, if a sequence A = (a0, au a2,...) of O's and l's has a certain limiting relative frequency p of l's to number of places, then every (infinite) sequence, composed of members of the sequence  ...  Let P(i) = limn^x Q(i,ri), where this has been seen to be well defined. Then by the lemma P={i\P(i)} eSí+2 n IIi+2. This proves Theorem 2.  ... 
doi:10.2307/1994579 fatcat:4smxn7x7l5hnzhhtt74dpyvp4e

The Kleene hierarchy classification of recursively random sequences

D. W. Loveland
1966 Transactions of the American Mathematical Society  
We confine our attention to sequences of O's and l's and then make the natural correspondence between sequences and sets by associating with the infinite sequence a0, alt a2,... the set {/1 a¡= 1}.  ...  In essence, if a sequence A = (a0, au a2,...) of O's and l's has a certain limiting relative frequency p of l's to number of places, then every (infinite) sequence, composed of members of the sequence  ...  Let P(i) = limn^x Q(i,ri), where this has been seen to be well defined. Then by the lemma P={i\P(i)} eSí+2 n IIi+2. This proves Theorem 2.  ... 
doi:10.1090/s0002-9947-1966-0207562-2 fatcat:5dsurdsvivcl5fm7choksthdwe

Induction, pure and simple

Peter Kugel
1977 Information and Control  
that is analytic in the sense that the theories it puts forth as sound will be sound in "all possible worlds." (3) If we use the machinery of the trial and error machine (or the machinery required to  ...  abstract point of view and to ask some questions about the structure of this process.  ...  We call a mechanism a trial-and-error machine [the term "trial and error" is due to Putnam (1965) ] if its output, for the input x, is defined to be the last integer it computes, or, to be more precise  ... 
doi:10.1016/s0019-9958(77)90175-9 fatcat:ji6sj6exhraexc6bjg4ojxhl2q

On the Identification of Quantifiers' Witness Sets: A Study of Multi-quantifier Sentences

Livio Robaldo, Jakub Szymanik, Ben Meijering
2014 Journal of Logic, Language and Information  
The latter seems to capture the proper interplay between the semantics and the pragmatics of multi-quantifier sentences, provided that witness sets are selected on pragmatic grounds.  ...  Two kinds of maximization have been proposed in the literature: 'Local' and 'Global' maximization.  ...  A good survey of the alternative solutions is given by Stanley and Szabò (2000) .  ... 
doi:10.1007/s10849-014-9197-9 fatcat:7lgmbwryb5baddqvyjz3byq62m

OpenJML: Software verification for Java 7 using JML, OpenJDK, and Eclipse

David R. Cok
2014 Electronic Proceedings in Theoretical Computer Science  
OpenJML is a tool for checking code and specifications of Java programs.  ...  The implementation demonstrates the value of integrating specification tools directly in the software development IDE and in automating as many tasks as possible.  ...  It is convenient to launch verification attempts of all the methods in a system, perhaps in parallel, returning later to address individually the methods and classes that show problems.  ... 
doi:10.4204/eptcs.149.8 fatcat:sjeyvbvotrf3vhuj7pp6ayku7i

The May meeting in Yosemite

J. W. Green
1954 Bulletin of the American Mathematical Society  
If, furthermore, fe = l, the number of meet-irreducibles and the number of join-irreducibles in L are equal. The abstract Moebius function is employed to obtain the results.  ...  ALGEBRA AND THEORY OF NUMBERS 548. S. P. Avann : Dual symmetry of projective sets in a finite modular lattice.  ...  The theory applies also to the discretization error connected with solutions of boundary value problems by random walks that are not restricted to the points of any net.  ... 
doi:10.1090/s0002-9904-1954-09827-0 fatcat:3kcufmshnfg4hlcdtqelh3klwm

On the grammar and processing of proportional quantifiers: most versus more than half

Martin Hackl
2009 Natural Language Semantics  
forms for seemingly equivalent statements of the form most A B and more than half of the A B.  ...  Proportional quantifiers have played a central role in the development of formal semantics because they set a bench mark for the expressive power needed to describe quantification in natural language (  ...  Coarseness of GQT According to GQT, quantification in natural language is a form of second order predication where quantifiers such as every student denote predicates of predicates (or sets of sets) and  ... 
doi:10.1007/s11050-008-9039-x fatcat:tqmoayqb4zcgnfemcaswrqaz74

The April meeting in New York

R. D. Schafer
1957 Bulletin of the American Mathematical Society  
If the ƒ* are constants and the order of A exceeds that of B or if r = 3 and the order of A exceeds that of B by at least 2, then the Li are independent. (Received February 18, 1957.) 403.  ...  Malcolm Goldman : A coset-like decomposition relative to certain rings of operators.  ...  Let Vi (i^4) be the set of sentences true in all 3C t -models. Kreisel and Mostowski (cf. Fund. Math. vol. 42 (1955) p. 125) proved Fo^Fi (assuming more complicated predicates).  ... 
doi:10.1090/s0002-9904-1957-10124-4 fatcat:ic6zy7tgvjeszdyckhzxdqpqiy

Discriminator varieties and symbolic computation

Stanley Burris
1992 Journal of symbolic computation  
two unifiable terms), and 2. every mathematical problem can be routinely cast in the forint Pl ~ ql , 9 9 Pk ~ qk hnplies the equation x ~ y. (2) shows that Birkhoff's five rules of inference for equational  ...  We look at two aspects of dlscrLminator varieties which could be of considerable interest in symbolic computation: 1, discriminator varieties are unitary (i.e., there is always a most general unifier of  ...  The method we used to find initial unifiers in the examples below was to use trial and error on the collection S1 of one-generated simple algebras in V [or the collection So of zero-generated simples if  ... 
doi:10.1016/s0747-7171(08)80089-2 fatcat:ckjujawtgzb53br24dmarotgba

On consistency and existence in mathematics [article]

Walter Dean
2020 arXiv   pre-print
The question is related historically to the formulation, proof, and reception of Gödel's Completeness Theorem.  ...  This paper engages the question Does the consistency of a set of axioms entail the existence of a model in which they are satisfied? within the frame of the Frege-Hilbert controversy.  ...  In other words A is ∆ 0 2 just in case there is a so-called trial and error procedure for deciding n ∈ A -i.e. one for which membership can be determined by following a guessing procedure which may make  ... 
arXiv:2007.10167v1 fatcat:72llgzqmenhivmhgorpdn5xohq

Quantification at the Syntax-Semantics Interface: Greek Every NPs (University of Patras, 2014)

Anna-Maria Margariti
2015 Journal of Greek Linguistics  
The other one is between the sentential operator and the relevant feature on Q but also on TP/ vP. The quantificational chains formed are argued to be, to some extent, similar to that of wh-chains.  ...  In Chapter 1, I present the essential syntactic and semantic background, as well as an outline of my proposal to the riddle of every and (o)kathe NPs interpretational variability.  ...  Because of the uncontestable universal/distributive status of the x operator in predicate logic and the close affinity between the GQ theory in logic (Mostowski 1957 ) and in semantics (Montague 1970  ... 
doi:10.1163/15699846-01501006 fatcat:h6mw2z6bq5dwpkznfoctzjcwk4
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