Akira Nakamura. On an axiomatic system of the infinitely many-valued threshold logics. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), pp. 71–76. - Akira Nakamura. On the infinitely many-valued threshold logics and von Wright's system M″. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), pp. 147–164. - Akira Nakamura. A note on truth-value functions in the infinitely many-valued logics. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), vol. 9 (1963), pp. 141–144. - Akira Nakamura. On a simple axiomatic system of the infinitely many-valued logic based on ∧, →. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), pp. 251–263. - Akira Nakamura. On an axiomatic system of the infinitely many-valued threshold predicate calculi. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), pp. 321–239. - Akira Nakamura. Truth-value stipulations for the von Wright system M′ and the Heyting system. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), vol. 10 (1964), pp. 173–183.

1965 ◽  
Vol 30 (3) ◽  
pp. 374-375
Author(s):  
Arto Salomaa
Keyword(s):  
Axiomatic System ◽  
Value Functions ◽  
Truth Value

A Probabilistic Propositional Logic System is an Event Semantics for Classical Formal System of Propositional Calculus

2013 ◽  
Vol 427-429 ◽  
pp. 1917-1923
Author(s):  
Hong Lan Liu ◽  
De Zheng Zhang
Keyword(s):  
Formal System ◽  
Propositional Calculus ◽  
Semantic Interpretation ◽  
Probabilistic Logic ◽  
Value Functions ◽  
Event Semantics ◽  
Set Inclusion ◽  
Set Operations ◽  
Truth Value ◽  
Logic System

The well formed formulas (wffs) in classical formal system of propositional calculus (CPC) are only some formal symbols, whose meanings are given by an interpretation. A probabilistic logic system, based on a probabilistic space, is an event semantics for CPC, in which set operations are the semantic interpretations for connectives, event functions are the semantic interpretations for wffs, the event (set) inclusion is the semantic interpretation for tautological implication, and the event equality = is the semantic interpretation for tautological equivalence. CPC is applicable to probabilistic propositions completely. Event calculus instead of truth value (probability) calculus can be performed in CPC because there arent truth value functions (operators) to interpret all connectives correctly.

On Characterizing Unary Probability Functions and Truth-Value Functions

1985 ◽  
Vol 15 (1) ◽  
pp. 19-24 ◽  
Author(s):  
Hugues Leblanc
Keyword(s):  
Value Functions ◽  
Probability Functions ◽  
Truth Value ◽  
Customary Manner

Consider a language SL having as its primitive signs one or more atomic statements, the two connectives ‘∼’ and ‘&,’ and the two parentheses ‘(’ and ‘)’; and presume the extra connectives ‘V’ and ‘≡’ defined in the customary manner. With the statements of SL substituting for sets, and the three connectives ‘∼,’ ‘&,’and ‘V’ substituting for the complementation, intersection, and union signs, the constraints that Kolmogorov places in [1] on (unary) probability functions come to read:K1. 0 ≤ P(A),K2. P(∼(A & ∼A)) = 1,K3. If ⊦ ∼(A & B), then P(A ∨ B) = P(A) + P(B),K4. If ⊦ A ≡ B, then P(A) = P(B).2

Axiom schemes for m-valued propositions calculi

1945 ◽  
Vol 10 (3) ◽  
pp. 61-82 ◽  
Author(s):  
J. B. Rosser ◽  
A. R. Turquette
Keyword(s):  
Propositional Calculus ◽  
Value Functions ◽  
Truth Values ◽  
Truth Value ◽  
Propositional Calculi

In an m-valued propositional calculus, or a formalization of such a calculus, truth-value functions are allowed to take any truth-value t where 1 ≦ t ≦ m and m ≧ 2. In working with such calculi, or formalizations thereof, it has been decided to distinguish those truth-values which it is desirable for provable formulas to have from those which it is not desirable for provable formulas to have. The first class of truth-values is called designated and the second undesignated. This specification of certain of the m truth-values as designated and the remainder as undesignated is one of the distinguishing characteristics of m-valued propositional calculi, and it should be observed at the outset that two m-valued propositional calculi will be considered to differ even if they differ only in respect to the number of truth-values which are taken as designated.

Hilbert-style proof Calculus for Propositional Logic in ABC notation

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Propositional Logic ◽  
Inference Rule ◽  
Modus Ponens ◽  
Axiomatic System ◽  
First Contact

All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

How Art Works

2018 ◽  
Author(s):  
Ellen Winner
Keyword(s):  
Statistical Analysis ◽  
Data Collection ◽  
Social Science ◽  
Modern Art ◽  
Hard Work ◽  
Objective Truth ◽  
The Arts ◽  
Art Form ◽  
Art Works ◽  
Truth Value

This book is an examination of what psychologists have discovered about how art works—what it does to us, how we experience art, how we react to it emotionally, how we judge it, and what we learn from it. The questions investigate include the following: What makes us call something art? Do we experience “real” emotions from the arts? Do aesthetic judgments have any objective truth value? Does learning to play music raise a child’s IQ? Is modern art something my kid could do? Is achieving greatness in an art form just a matter of hard work? Philosophers have grappled with these questions for centuries, and laypeople have often puzzled about them too and offered their own views. But now psychologists have begun to explore these questions empirically, and have made many fascinating discoveries using the methods of social science (interviews, experimentation, data collection, statistical analysis).

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