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### One-and-a-halfth-order logic

Murdoch J. Gabbay, Aad Mathijssen
2006 Proceedings of the 8th ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '06
We exhibit both algebraic 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!  ...

### One-and-a-Halfth Order Terms: Curry-Howard and Incomplete Derivations [chapter]

Murdoch J. Gabbay, Dominic P. Mulligan
2008 Lecture Notes in Computer Science
To this end we use 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]

Jorge Pais, Álvaro Tasistro
2014 Lecture Notes in Computer Science
We present 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.  ...

### Bending the poggendorff parallels and the rules of inference: A note on brigell and uhlarik (1980)

Peter Wenderoth
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 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  ...

### Two-level Lambda-calculus

Murdoch J. Gabbay, Dominic P. Mulligan
2009 Electronical Notes in Theoretical Computer Science
Lambda-abstraction 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] .  ...

### 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.  ...

### Limits on the applicability of signal detection theories

Allen Parducci, Arthur J. Sandusky
1970 Perception & Psychophysics
Two auditory signals were presented in random sequencesin which the more intense signalcame 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.  ...

### What is an Infinite Regress Argument?

Claude Gratton
1996 Informal Logic
I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present 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.  ...

### What is an Infinite Regress Argument? [chapter]

Claude Gratton
2009 Argumentation Library
I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present 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.  ...

### 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.  ...

### VLSI implementation of real-time parallel DCT/DST lattice structures for video communications

C.T. Chiu, R. K. Kolagotla, K.J.R. Liu, J. F. JaJa
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.  ...

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

Murdoch J. Gabbay, Aad Mathijssen
2007 Lecture Notes in Computer Science
In spite of this, we can axiomatise systems of 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.  ...

### 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.  ...

### Permissive-nominal logic

Gilles Dowek, Murdoch J. Gabbay
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-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').  ...

### Curry-Howard for incomplete first-order logic derivations using one-and-a-half level terms

Murdoch J. Gabbay, Dominic P. Mulligan
2010 Information and Computation
We apply 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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