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

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*? ...

##
###
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. ...

##
###
JSL volume 30 issue 1 Cover and Front matter

1965
*
Journal of Symbolic Logic (JSL)
*

. > 28

doi:10.1017/s0022481200057054
fatcat:cq6vhmsp7ffmnjyk4wnbt6jpmi
*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 ...##
###
The Kleene Hierarchy Classification of Recursively Random Sequences

1966
*
Transactions of the American Mathematical Society
*

We confine our attention

doi:10.2307/1994579
fatcat:4smxn7x7l5hnzhhtt74dpyvp4e
*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. ...##
###
The Kleene hierarchy classification of recursively random sequences

1966
*
Transactions of the American Mathematical Society
*

We confine our attention

doi:10.1090/s0002-9947-1966-0207562-2
fatcat:5dsurdsvivcl5fm7choksthdwe
*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. ...##
###
Induction, pure and simple

1977
*
Information and Control
*

that is analytic in

doi:10.1016/s0019-9958(77)90175-9
fatcat:ji6sj6exhraexc6bjg4ojxhl2q
*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 ...##
###
On the Identification of Quantifiers' Witness Sets: A Study of Multi-quantifier Sentences

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) . ...

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

2014
*
Electronic Proceedings in Theoretical Computer Science
*

OpenJML is

doi:10.4204/eptcs.149.8
fatcat:sjeyvbvotrf3vhuj7pp6ayku7i
*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*. ...##
###
The May meeting in Yosemite

1954
*
Bulletin of the American Mathematical Society
*

If, furthermore, fe = l,

doi:10.1090/s0002-9904-1954-09827-0
fatcat:3kcufmshnfg4hlcdtqelh3klwm
*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. ...##
###
On the grammar and processing of proportional quantifiers: most versus more than half

2009
*
Natural Language Semantics
*

forms for seemingly equivalent statements

doi:10.1007/s11050-008-9039-x
fatcat:tqmoayqb4zcgnfemcaswrqaz74
*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*...##
###
The April meeting in New York

1957
*
Bulletin of the American Mathematical Society
*

If

doi:10.1090/s0002-9904-1957-10124-4
fatcat:ic6zy7tgvjeszdyckhzxdqpqiy
*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*). ...##
###
Discriminator varieties and symbolic computation

1992
*
Journal of symbolic computation
*

two unifiable terms),

doi:10.1016/s0747-7171(08)80089-2
fatcat:ckjujawtgzb53br24dmarotgba
*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 ...##
###
On consistency and existence in mathematics
[article]

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 ...

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

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 ...

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