positive logic

positive logic

[′päz·əd·iv ′läj·ik]
Logic circuitry in which the more positive voltage (or current level) represents the 1 state; the less positive level represents the 0 state.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Positive Logic


logic in which the only arguments considered acceptable are those not connected with refutations, that is, with proofs of the falseness of propositions. Since the expression “A is false” is merely a variant of the expression ”not-A,” positive logic rejects any methods of introducing negation that involve methods of indirect proof, including proof by contradiction. It also rejects explicit definitions of negation of the type ⌝ A = dfA ⊃ f, where ⌝ is the negation symbol, 3 indicates implication, and f is a propositional variable or some “admissible” absurd assertion. Thus, positive logic may be said to be a logic without negation.

The logical laws corresponding to correct arguments in positive logic (or the rules codifying the methods of such arguments) are described and cataloged in suitable logical calculi. The most important of these logical calculi are the positive implicative propositional calculus with the single logical operation of implication and the complete positive propositional calculus with conjunction, disjunction, implication, and equivalence.

The positive implicative propositional calculus is given by means of two axiom schemes:

(1) A ⊃ (B ⊃ A)

(2) (A ⊃ (B ⊃ C)) ⊃ ((A ⊃ B) ⊃ (A ⊃ C))

and the rules of modus ponens. The complete positive propositional calculus is given by adding to schemes (1) and (2) the following:

(3) (A & B)A

(4) (A & B)B

(5) A(B ⊃ (A & B))

(6) (AC) ⊃ ((8 ⊃ C)((A V B)C))

(7) A(A V B)

(8) B(A V B)

An equivalence is defined to be an abbreviation for the expression (AB) & (BA). More powerful logical calculi are obtained from the calculi of positive logic by successive nonconservative extensions of their systems of axioms or rules of derivation. Thus, attaching the axiom scheme

(9) (AB) ⊃ ((A ⊃ ⌝ B) ⌝ A)

or the corresponding rule of reductio ad absurdum to (1) and (2) gives Kolmogorov’s minimal logic (1925). The analogous addition to the complete positive propositional calculus gives Johansson’s minimal logic (1936). By appending to Johansson’s minimal logic the scheme

(10) ⌝ A ⊃ (A ⊃ B)

(a contradiction will entail an arbitrary assertion) and the scheme

(11) ⊃ A V A

(the law of the excluded middle), we obtain the intuitionist propositional logic and classical propositional logic, respectively.

Since all laws of positive logic are valid (provable) in intuitionist and classical logic—the converse naturally is untrue—positive calculi usually are considered subsystems; generally they are considered partial systems. It is significant, however, that positive calculi, taken “in and of themselves,” and “the same” calculi “within” a more powerful logic are calculi with a different semantics for the logical connectives (operations). The semantics for the former is determined only by the calculus’ own axioms or rules for the use of connectives, whereas the semantics for the latter is inherited from the more powerful logic.


Church, A. Vvedenie ν matematicheskuiu logiku, vol. 1, subsec. 26. Moscow, 1960. (Translated from English.)
Rasiowa, H. and R. Sikorski. Matematika metamatematiki, ch. 11, subsecs. 1–6. Moscow, 1972. (Translated from English.)


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

positive logic

The use of low voltage for a 0 bit and high voltage for a 1 bit. Contrast with negative logic.
Copyright © 1981-2019 by The Computer Language Company Inc. All Rights reserved. THIS DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction is strictly prohibited without permission from the publisher.
References in periodicals archive ?
Huston, TX, November 12, 2015 --(PR.com)-- Online-Devices have announced a new 48-ch Digital I/O Controller with a Positive Logic and Over-Current Protection on all outputs.
Positive Logic Outputs with an Over-Current Protection on each output makes the IA-3125-U2i a real innovative product with a tremendous impact both on the ease of use and on the expected decreasing failures while using it.
* Optional configurations that include various pin lengths to eliminate secondary process for trimming pins, positive logic control, and conformal coating.
As opposed to this apophatic negativity, Pound proposes a positive logic of the gift, which emphasizes 'not abandonment from but abandonment to God' (49), and the overwhelming 'superabundance' (140)--not lack--of the world.
In addition, the positive logic remote on/off control and inverter-operation-good functions provide greater flexibility in the start-up or shutdown sequencing and diagnostics of the power system.
There is a "positive logic" for Russia in developing this relationship.
Floating the FETs in this manner allows for the use of positive logic (0/+5 V) to drive the RF circuit.
Their topics include modal logic in the model sense of modality, a topological view of Linstrom's theorem for positive logics, the size of a formula as a measure of complexity, universal structures with forbidden homomorphisms, saturating the random graph with an independent family of small range, and the twin continua of inductive methods.

Full browser ?