scholarly journals Generalizing the Depth Relevance Condition: Deep Relevant Logics Not Included in R-Mingle

2014 ◽  
Vol 55 (1) ◽  
pp. 107-127 ◽  
Author(s):  
Gemma Robles ◽  
José M. Méndez
Keyword(s):  
Relevant Logics ◽  
Relevance Condition ◽  
Depth Relevance

Strong Depth Relevance

2021 ◽  
Vol 18 (6) ◽  
pp. 645-656
Author(s):  
Shay Allen Logan
Keyword(s):  
Propositional Variable ◽  
Half Century ◽  
Relevant Logics ◽  
Depth Relevance

Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways.

TRANSLATIONS BETWEEN LINEAR AND TREE NATURAL DEDUCTION SYSTEMS FOR RELEVANT LOGICS

2021 ◽  
pp. 1-22
Author(s):  
SHAWN STANDEFER
Keyword(s):  
Natural Deduction ◽  
The Other ◽  
Relevant Logics

Abstract Anderson and Belnap presented indexed Fitch-style natural deduction systems for the relevant logics R, E, and T. This work was extended by Brady to cover a range of relevant logics. In this paper I present indexed tree natural deduction systems for the Anderson–Belnap–Brady systems and show how to translate proofs in one format into proofs in the other, which establishes the adequacy of the tree systems.

scholarly journals INFINITARY PROPOSITIONAL RELEVANT LANGUAGES WITH ABSURDITY

2017 ◽  
Vol 10 (4) ◽  
pp. 663-681
Author(s):  
GUILLERMO BADIA
Keyword(s):  
Expressive Power ◽  
Interpolation Theorem ◽  
Boolean Logic ◽  
Isomorphism Theorem ◽  
Strong Completeness ◽  
Lack Of Compactness ◽  
Relevant Logics ◽  
Beth Definability ◽  
Beth Definability Property

AbstractAnalogues of Scott’s isomorphism theorem, Karp’s theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An “interpolation theorem” (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L∞ω holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.

The Moderating Role of Personal Relevance on Differential Priming of Anxiety and Sadness on Perceived Travel Risk: A Replication

2009 ◽  
Vol 104 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Wen-Bin Chiou ◽  
Ming-Hsu Chang ◽  
Chien-Lung Chen
Keyword(s):  
Decision Making ◽  
Risk Taking ◽  
Personal Relevance ◽  
Risk Averse ◽  
Mood Repair ◽  
Neutral Mood ◽  
Motivational Influences ◽  
Relevance Condition ◽  
Moderating Role

Raghunathan and Pham conducted a pioneer study in 1999 on the motivational influences of anxiety and sadness on decision making and indicated that anxiety would motivate individuals to be risk averse, whereas sadness would motivate individuals to be risk taking. A replication study was employed in the domain of perceived travel risk. Compared to participants in a neutral mood, anxious participants showed higher perceived travel risk than sad participants. Moreover, the differential effect of anxiety and sadness on perceived travel risk was only pronounced under the high personal relevance condition, in which participants made personal decisions and expected that they would be affected by the outcomes. In general, the results extend the notion proposed by Raghunathan and Pham suggesting that travelers' implicit goals primed by anxiety or sadness used for mood-repair purposes appear to be moderated by personal relevance.

scholarly journals Boolean negation and non-conservativity II: The variable-sharing property

2020 ◽  
Author(s):  
Tore Fjetland Øgaard
Keyword(s):  
Classical Logic ◽  
Relevant Logic ◽  
Relevant Logics ◽  
Acute Form ◽  
Vast Range ◽  
Boolean Extension

Abstract Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the Boolean extended logic.

scholarly journals Boolean negation and non-conservativity III: the Ackermann constant

2020 ◽  
Author(s):  
Tore Fjetland Øgaard
Keyword(s):  
Relevant Logics

Abstract It is known that many relevant logics can be conservatively extended by the truth constant known as the Ackermann constant. It is also known that many relevant logics can be conservatively extended by Boolean negation. This essay, however, shows that a range of relevant logics with the Ackermann constant cannot be conservatively extended by a Boolean negation.

E, R AND γ

1969 ◽  
Vol 34 (3) ◽  
pp. 460-474 ◽  
Author(s):  
Robert K. Meyer ◽  
J. Michael Dunn
Keyword(s):  
Relevant Implication ◽  
Relevant Logics

By γ, we mean the rule, “From ├ A and ├ Ā V B, infer ├ B”.1 This rule has played an important and a controversial role in a set of relevant logics free of certain well-known paradoxes of implication, like AĀ-→B and A-→(B-→B). Among these logics we count the pioneering systems of strenge Implikation presented by Ackermann in [1],2 as well as the Anderson-Belnap systems E of entail-ment and R of relevant implication.3

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