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One-and-a-halfth-order logic

2006
*
Proceedings of the 8th ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '06
*

We exhibit both algebraic

doi:10.1145/1140335.1140359
dblp:conf/ppdp/GabbayM06
fatcat:sbvrcyvv7bac5h5p2wjdmbdwia
*and*sequent specifications of*one*-*and*-*a*-*halfth*-*order**logic*derivability, show them equivalent, show that the derivations satisfy cut-elimination,*and*prove correctness of an interpretation ... We present*one*-*and*-*a*-halfthorder*logic*, in which these concepts are made explicit. ... Perhaps*one*day*one*-*and*-*a*-*halfth*-*order**logic*too will be formalised in*a*framework! ...##
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One-and-a-Halfth Order Terms: Curry-Howard and Incomplete Derivations
[chapter]

2008
*
Lecture Notes in Computer Science
*

To this end we use

doi:10.1007/978-3-540-69937-8_16
fatcat:igzf33dnerfernchhzherbpmka
*a**one*-*and*-*a*-*halfth**order*technique based*on*nominal terms, with two levels of variable. ...*A*Technical appendix We will use the following fact without comment: Lemma 22 If Γ r is closed (so Γ mentions no unknowns*and*the freshness context is empty)*and*Γ r is typable, then r mentions no unknowns ... We use*a*'*one*-*and*-*a*-*halfth**order*' syntax, building*on*ideas from nominal terms*and**one*-*and*-*a*-*halfth**order**logic*: atoms model variable symbols*and*can be quantified (we use atoms to model both type*and*...##
###
Novel Didactic Proof Assistant for First-Order Logic Natural Deduction
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-319-07482-5_42
fatcat:tloqap55g5b23dm44ysd475bli
*a*proof assistant designed to help learning formal proof, particularly in the system of Natural Deduction for First-*Order**Logic*. ... It possesses*a*graphical interface presenting proofs as trees*and*handles multiple simultaneous derivations that can be dragged*and*dropped into*one*another. ... For accomplishing this we have based ourselves*on*the already mentioned*One*-*and*-*a*-*Halfth**Order**Logic*. ...##
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Bending the poggendorff parallels and the rules of inference: A note on brigell and uhlarik (1980)

1981
*
Perception & Psychophysics
*

This analysis of the results gains some credence from the fact that, even then, the largest effect obtained was 3-4 deg, about

doi:10.3758/bf03207296
pmid:7267281
fatcat:tvhlgxg25van3m2d43x37ojb3a
*halfthe*usual, full Poggendorff effect. ... Consequently, since angular effects might summate to reverse the illusions in 10, depth cues might reduce the effect in lA,*and*symmetry might eradicate the illusion in lC, it is hardly surprising that ... Brigell*and*Uhlarik found that: (*a*) largest errors, in the usual Poggendorff direction, occurred when (3 was 120 deg (Figure IB),*and*these were*on*the*order*of 3 to 4 deg; (b) quite small errors were ...##
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Two-level Lambda-calculus

2009
*
Electronical Notes in Theoretical Computer Science
*

Lambda-abstraction

doi:10.1016/j.entcs.2009.07.018
fatcat:wdgarvh7qjbsdotns5lqbfm63e
*and*beta-reduction exist for both levels.*A*level 2 beta-reduct, triggering*a*substitution of*a*term for*a*level 2 variable, does not avoid capture for level 1 abstractions. ... In doing this we take*a*step towards longer-term goals of developing*a*foundation for theorem-provers which directly support reasoning in the style of nominal rewriting*and*nominal algebra,*and*towards ... We have used '-*and*-*a*-*halfth**order*', as in '*one*-*and*-*a*-*halfth**order**logic*' [17] or 'two-*and*-*a*-*halfth**order*lambda-calculus' [16] . ...##
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Page 217 of Phrenological Journal and Science of Health Vol. 84, Issue 4
[page]

1887
*
Phrenological Journal and Science of Health
*

. |

*AND*SCIENCE OF HEALTH. 217*logical*indication; portions of*a*bulb of*a*lily furnished further proof. ...*A*cov- ering of cloth is then put*on**and*secured with*a*few stitches, or tied with*a*tape or string. The paper soon dries*and*becomes hard*and*stiff. ...##
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Limits on the applicability of signal detection theories

1970
*
Perception & Psychophysics
*

Two auditory signals were presented in random sequencesin which the more intense signalcame

doi:10.3758/bf03210134
fatcat:wchwwzgkzjcc7fjf4qbuvpzfme
*on*.2, .5, or.8*a*/the trials.Eech trialbegan with an intermediate tone which was identified in the instructions ... as either the standard for comparison or simply as*a*warningtone. ... First-*order*sequential effects were not found for either of the present tasks, accuracy*on*each signal being virtually independent of which signal had been presented*on*the preceding trial. ...##
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What is an Infinite Regress Argument?

1996
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Informal Logic
*

I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present

doi:10.22329/il.v18i2.2380
fatcat:h65ylabthngu3gdm3uu5ui4eay
*a*working hypothesis of the nature*and*derivation of an infinite regress; apply this working ... hypothesis to various infinite regress arguments to explain why they fail to entail an infinite regress; describe*a*common mistake in attempting to derive certain infinite regresses;*and*examine how infinite ... C(2): MaPI is*halfthe*size ofthe U.S.,*and*covers*halfthe*U.S .. C(3): MaPI is*a*significant geographical feature. ...##
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What is an Infinite Regress Argument?
[chapter]

2009
*
Argumentation Library
*

I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present

doi:10.1007/978-90-481-3341-3_1
fatcat:lxg4dc7o7nfvlfrdzziz36sko4
*a*working hypothesis of the nature*and*derivation of an infinite regress; apply this working ... hypothesis to various infinite regress arguments to explain why they fail to entail an infinite regress; describe*a*common mistake in attempting to derive certain infinite regresses;*and*examine how infinite ... C(2): MaPI is*halfthe*size ofthe U.S.,*and*covers*halfthe*U.S .. C(3): MaPI is*a*significant geographical feature. ...##
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Page 4281 of Psychological Abstracts Vol. 84, Issue 9
[page]

1997
*
Psychological Abstracts
*

(Private Practice, Eastwood, NSW, Aus- tralia) Comment: Towards

*a**one*-*and*-*a*-*halfth**order*practice: Rehabilitating pragmatics. Journal of Family Therapy, 1996(Aug), Vol 18(3), 243-248. ... —Comments*on**A*. C. James*and*M. Vereker’s (see record 84-32196) article of the use of family therapy with patients diagnosed with borderline personality dis-*order*. ...##
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VLSI implementation of real-time parallel DCT/DST lattice structures for video communications

1992
*
Workshop on VLSI Signal Processing
*

*A*parallel lattice structure that can dually generate the 1-D DCT

*and*DST is proposed. ... This realization of the lattice module using 2pm double metal CMOS technology is capable of processing

*a*t

*a*data rate of 116Mb/s in rea 1-time. ... This is fabricated in

*a*die of size 6800X x 4600X

*and*packaged in

*a*40-pin chip. Both

*logical*

*and*timing simulations were performed

*on*the this chip. ...

##
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A Formal Calculus for Informal Equality with Binding
[chapter]

2007
*
Lecture Notes in Computer Science
*

In spite of this, we can axiomatise systems of

doi:10.1007/978-3-540-73445-1_12
fatcat:wntzp5iacrhtzfifjyyxcsae6m
*logic**and*computation such as first-*order**logic*or the lambda-calculus in*a*very direct*and*natural way. ... We base our*logic**on*equality, probably the simplest available judgement form. ... We made*a*start in that direction by designing*one*-*and*-*a*-*halfth**order**logic*[10] . However that system does not allow quantification of unknowns,*and*we are now working*on*lifting that restriction. ...##
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Page 60 of The Athenaeum Vol. , Issue 1368
[page]

1854
*
The Athenaeum
*

FORMAL

*LOGIC*; or, the Calculus of Infer- ence, Necessary*and*Probable. 8vo. 68. 6d. 4. ... (*halfthe*Work) now ready, 11. 16s, cloth lettered. SMITH'S DICTIONARY of GREEK*and*ROMAN ANTIQUITIES. By Various Writers. ...##
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Permissive-nominal logic

2010
*
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10
*

All this gives PNL much of the expressive power of higher-

doi:10.1145/1836089.1836111
dblp:conf/ppdp/DowekG10
fatcat:v4fdwmz2zjgcpivynpvoq3sckq
*order**logic*, but terms, derivations*and*models of PNL are first-*order*in character,*and*the*logic*seems to strike*a*good balance between expressivity ... Like first-*and*higher-*order**logic**and*unlike other nominal*logics*, equality reasoning is not necessary to α-rename. ...*One*-*and*-*a*-*halfth**order**logic*from [17] This*logic*is designed to represent schematic first-*order*reasoning (firstorder derivations in the presence of 'unknown predicates'). ...##
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Curry-Howard for incomplete first-order logic derivations using one-and-a-half level terms

2010
*
Information and Computation
*

We apply

doi:10.1016/j.ic.2009.09.003
fatcat:srn42hci2jgnhavhvcisl4hwwe
*a**one*-*and*-*a*-half level technique based*on*nominal terms to construct*a*Curry-Howard correspondence for first-*order**logic*. ... Our techniques are not specifically tailored to first-*order**logic**and*the same ideas should be applicable without any essential new difficulties to similar*logical*systems. ... We use*a**one*-*and*-*a*-half level syntax building*on*ideas from*one*-*and*-*a*-*halfth**order**logic*[19] : variables of level*one*model variable symbols*and*can be quantified (we use variables of level*one*to model ...
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