Relevance Logic

Dunn, J. Michael; Restall, Greg

doi:10.1007/978-94-017-0460-1_1

Cited by 278 publications

(90 citation statements)

References 88 publications

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“…For this, we follow the primary consideration behind relevance logics and consider variations of the attack rules, according to which the attacking sequent should contain information which is relevant to the attacked sequent (see, e.g. Dunn & Restall, 2002). This is enforced by the variable sharing property, a principle that in our case requires that the support sets of the attacking and the attacked sequents should share variables, and so the former is 'relevant' for the latter.…”

Section: Relevant Attacksmentioning

confidence: 99%

“…This induces a general and uniform approach not only for introducing arguments, but also for eliminating them. Furthermore, in addition to known attack relations that are 'imported' to our framework (which are discussed in Arieli, 2013), we also introduce new types of attack relations, like attacks incorporating different kinds of modal operators, quantitative measurements, and attacks that are based on relevance considerations, implementing the well-known principle of variable sharing from relevance logics (Dunn and Restall, 2002) and applying it for argumentation reasoning.…”

Section: Introductionmentioning

confidence: 99%

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Sequent-based logical argumentation

Arieli¹,

Straßer²

2015

Argument & Computation

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We introduce a general approach for representing and reasoning with argumentation-based systems. In our framework arguments are represented by Gentzen-style sequents, attacks (conflicts) between arguments are represented by sequent elimination rules, and deductions are made according to Dung-style skeptical or credulous semantics. This framework accommodates different languages and logics in which arguments may be represented, allows for a flexible and simple way of expressing and identifying arguments, supports a variety of attack relations (including those that reflect relevance or quantitative considerations), and is faithful to standard methods of drawing conclusions by argumentation frameworks. Altogether, we show that argumentation theory may benefit from incorporating proof theoretical techniques and that different non-classical formalisms may be used for backing up intended argumentation semantics.

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Section: Relevant Attacksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sequent-based logical argumentation

Arieli¹,

Straßer²

2015

Argument & Computation

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“…A meaningful conditional deduction requires that the antecedent is relevant to the consequent, or in other words that the consequent depends on the antecedent, as explicitly expressed in relevance logics [5]. Conditionals that are based on the dependence between consequent and antecedent are considered to be universally valid (and not truth functional), and are called logical conditionals [3].…”

Section: Discussionmentioning

confidence: 99%

Conditional Deduction Under Uncertainty

Jøsang¹,

Pope²,

Daniel

2005

Lecture Notes in Computer Science

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Abstract. Conditional deduction in binary logic basically consists of deriving new statements from an existing set of statements and conditional rules. Modus Ponens, which is the classical example of a conditional deduction rule, expresses a conditional relationship between an antecedent and a consequent. A generalisation of Modus Ponens to probabilities in the form of probabilistic conditional inference is also well known. This paper describes a method for conditional deduction with beliefs which is a generalisation of probabilistic conditional inference and Modus Ponens. Meaningful conditional deduction requires a degree of relevance between the antecedent and the consequent, and this relevance can be explicitly expressed and measured with our method. Our belief representation has the advantage that it is possible to represent partial ignorance regarding the truth of statements, and is therefore suitable to model typical real life situations. Conditional deduction with beliefs thereby allows partial ignorance to be included in the analysis and deduction of statements and hypothesis.

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“…Mares' SEP article [11] lists three types of such interpretations. According to Dunn's version, Rxyz is best understood to say that "the combination of the pieces of information in x and y ... is a piece of information in z" [5]. Notions such as "information channel" or "information link" invoked by Restall and Mares also make sense [9,10,13] under this interpretation.…”

Section: Ternary Relation Routley-star and Negation As Modalitymentioning

confidence: 96%

Understanding Negation Implicationally in the Relevant Logic R

Onishi

2016

Stud Logica

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A star-free relational semantics for relevant logic is presented together with a sound and complete sequent proof theory (display calculus). It is an extension of the dualist approach to negation regarded as modality, according to which de Morgan negation in relevant logic is better understood as the confusion of two negative modalities. The present work shows a way to define them in terms of implication and a new connective, co-implication, which is modeled by respective ternary relations. The defined negations are confused by a special constraint on ternary relation, called the generalized star postulate, which implies definability of the Routley star in the frame. The resultant logic is shown to be equivalent to the well-known relevant logic R. Thus it can be seen as a reconstruction of R in the dualist framework.The defining feature of display calculus is the display property that every substructure of a sequent can be "displayed" through display rules. Cut elimination theorem can be proved in a generic way based on this property. Definition 4.3. (Antecedent/succedent parts) In X Y , we say X is an antecedent part (AP) and Y is a succedent part (SP). We define:• If W ; Z is an AP (SP) in X Y , so are W and Z, and • In any substructure W > Z of X Y , W (Z) is an AP (SP) in X Y .Definition 4.4. We say two sequents are display equivalent if they are derivable from each other using only display rules.

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Relevance Logic

Cited by 278 publications

References 88 publications

Sequent-based logical argumentation

Sequent-based logical argumentation

Conditional Deduction Under Uncertainty

Understanding Negation Implicationally in the Relevant Logic R

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