On a Theory of Weak Implications

Mitsuhiro Okada

doi:10.2307/2274438

Predicting Game-Attending Behavior in Amateur Athletes: The Moderating Role of Intention Stability

Psychological Reports ◽

10.2466/14.05.pr0.113x25z4 ◽

2013 ◽

Vol 113 (2) ◽

pp. 420-434 ◽

Cited By ~ 3

Author(s):

Wan Chen Lu ◽

Chih-Fu Cheng ◽

Lung Hung Chen

Keyword(s):

Behavioral Intention ◽

Behavioral Control ◽

Hierarchical Regression ◽

Perceived Behavioral Control ◽

Attending Behavior ◽

And Behavior ◽

Weak Implications ◽

The Relationship ◽

Moderating Role

The theory of planned behavior is a well-established theory in predicting human behavior. However, there is evidence of an inconsistent relationship between intention and behavior. Therefore, the purpose of the current study is to further investigate the gap between intention and behavior. The study proposes intention stability as the moderator. Participants ( N=154, M age = 23 yr., SD = 6.7) were recruited from Internet volleyball forums and local volleyball courts in Taiwan. Multiple hierarchical regression was used to analyze the data. The results indicated that perceived behavioral control significantly predicted game-attending behavior through intention. However, attitude and subjective norms did not significantly predict behavioral intention. In addition, intention stability moderated the relationship between intention and behavior and indicated the relationship between intention and behavior was strong when intention stability was high. On the contrary, when intention stability was low, the relationship between intention and behavior was weak. Implications and applications are discussed.

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Fuzzy Boundary Weak Implications

Communications in Computer and Information Science - Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations ◽

10.1007/978-3-319-91473-2_52 ◽

2018 ◽

pp. 611-622

Author(s):

Hua-Wen Liu ◽

Michał Baczyński

Keyword(s):

Weak Implications ◽

Fuzzy Boundary

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On a theory of weak implications

Journal of Symbolic Logic ◽

10.1017/s0022481200029030 ◽

1988 ◽

Vol 53 (1) ◽

pp. 200-211 ◽

Cited By ~ 2

Author(s):

Mitsuhiro Okada

Keyword(s):

Intuitionistic Logic ◽

General Setting ◽

Second Order ◽

Inference Rules ◽

Full Strength ◽

Circular Argument ◽

Logical Connectives ◽

Points Of View ◽

Weak Implications ◽

Order Extension

The purpose of this paper is to study logical implications which are much weaker than the implication of intuitionistic logic.In §1 we define the system SI (system of Simple Implication) which is obtained from intuitionistic logic by restricting the inference rules of intuitionistic implication. The implication of the system SI is called the “simple implication” and denoted by ⊃, where the simple implication ⊃ has the following properties:(1) The simple implication ⊃ is much weaker than the usual intuitionistic implication.(2) The simple implication ⊃ can be interpreted by the notion of provability, i.e., we have a very simple semantics for SI so that a sentence A ⊃ B is interpreted as “there exists a proof of B from A”.(3) The full-strength intuitionistic implication ⇒ is definable in a weak second order extension of SI; in other words, it is definable by help of a variant of the weak comprehension schema and the simple implication ⊃. Therefore, though SI is much weaker than the intuitionistic logic, the second order extension of SI is equivalent to the second order extension of the intuitionistic logic.(4) The simple implication is definable in a weak modal logic MI by the use of the modal operator and the intuitionistic implication ⇒ with full strength. More precisely, A ⊃ B is defined as the strict implication of the form ◽(A ⇒ B).In §1, we show (3) and (4). (2) is shown in §2 in a more general setting.Semantics by introduction rules of logical connectives has been studied from various points of view by many authors (e.g. Gentzen [4], Lorentzen [5], Dummett [1], [2], Prawitz [8]. Martin-Löf [7], Maehara [6]). Among them Gentzen (in §§10 and 11 of [4]) introduced such a semantics in order to justify logical inferences and the mathematical induction rule. He observed that all of the inference rules of intuitionistic arithmetic, except for those on implication and negation, are justified by means of his semantics, but justification of the inference rules on implication and negation contains a circular argument for the interpretation by introduction rules, where the natural interpretation of A ⊃ B by ⊃-introduction rule is “there exists a proof of B from A ” (cf. §11 of Gentzen [4]).

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