Proof-Theoretic Analysis of the Quantified Argument Calculus

Pavlović, Edi; Gratzl, Norbert

doi:10.1017/s1755020318000114

Cited by 9 publications

(21 citation statements)

References 6 publications

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“…the quantification was already restricted, and precisely in a manner that precludes the derivation of that formula which the free logic avoids. This demonstrates the point raised in [15],…”

Section: Comparison Of Fq B and Lk-quarc Bsupporting

confidence: 57%

“…To produce the free versions of the systems LK-Quarc B and LK-Quarc 2 we add the new rule for the existence predicate E!, replace the rules for the quantifiers, and also replace one of the identity rules in the latter of the two systems. In the interest of brevity, the full systems will not be laid out here, but the reader can find both those, and a thorough discussion of their metatheoretical properties, in [15].…”

Section: Free Quarcmentioning

confidence: 99%

“…We now turn towards establishing some metatheoretic properties of FQ B , first and foremost being the Cut elimination theorem. As everywhere in this paper, the proof is omitted, but it is a straightforward adaptation of the one found in [15].…”

Section: Metatheoretic Properties Of Fq Bmentioning

confidence: 99%

“…In this paper we shall therefore investigate interrelations between Quarc and free logic (especially with its negative variant). Furthermore, this paper approaches these interrelations with proof-theoretic methods and results of [15]. In it the authors claim that the rules of quantification in (the family of logics) Quarc resemble those of free logic.…”

Section: Introductionmentioning

confidence: 96%

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Free Logic and the Quantified Argument Calculus

Pavlović¹,

Gratzl²

2019

Philosophy of Logic and Mathematics

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The Quantified Argument Calculus (or Quarc for short) is a novel and peculiar system of quantified logic, particularly in its treatment of nonemptiness of unary predicates, as in Quarc unary predicates are never empty, and singular terms denote. Moreover, and as a consequence of this, the universally quantified formulas entail their corresponding particular ones, similar to existential import. But at the same time, Quarc eschews talk of existence entirely by having a particular quantifier instead of an existential one. To bring it back into consideration, we explicitly introduce the existence predicate, and modify the rules to make the existence assumption obvious. This, along with some modifications, leads to a version of negative free logic. A question that arises at this point, given that we are interested in free logic, is what happens when we remove the existence assumption on singular terms; here we can quite naturally choose the negative free logic framework as well. In this paper we shall therefore investigate interrelations between Quarc and free logic (especially with its negative variant), and approach these interrelations with proof-theoretic methods.

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“…the quantification was already restricted, and precisely in a manner that precludes the derivation of that formula which the free logic avoids. This demonstrates the point raised in [15],…”

Section: Comparison Of Fq B and Lk-quarc Bsupporting

confidence: 57%

Section: Free Quarcmentioning

confidence: 99%

Section: Metatheoretic Properties Of Fq Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

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Free Logic and the Quantified Argument Calculus

Pavlović¹,

Gratzl²

2019

Philosophy of Logic and Mathematics

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“…For example, this was the case with the free logic rules in [24, pp. 200-201], where the definitions make this reliance explicit, while here the quantifiers are restored to being independent of other operators (see also [22]).…”

Section: Advantages Of the Present Approachmentioning

confidence: 99%

A More Unified Approach to Free Logics

Pavlović

Gratzl

2020

J Philos Logic

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Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free logics usually reject the claim that names need to denote in (ii), and of the systems considered in this paper, the positive free logic concedes that some atomic formulas containing non-denoting names (namely self-identity) are true, while negative free logic rejects even the latter claim. Inclusive logics, which reject (i), are likewise considered. These logics have complex and varied axiomatizations and semantics, and the goal of this paper is to present an orderly examination of the various systems and their mutual relations. This is done by first offering a formalization, using sequent calculi which possess all the desired structural properties of a good proof system, including admissibility of contraction and cut, while streamlining free logics in a way no other approach has. We then present a simple and unified system of abstract semantics, which allows for a straightforward demonstration of the meta-theoretical properties, and offers insights into the relationship between different logics (free and classical). The final part of this paper is dedicated to extending the system with modalities by using a labeled sequent calculus, and here we are again able to map out the different approaches and their mutual relations using the same framework. Keywords Positive free logic • Negative free logic • Sequent calculus • G3 • Modal logic An anonymous reviewer has offered numerous suggestions which have, combined, amounted to a significant improvement of the paper, and for that we extend our gratitude. Special thanks goes to O. Foisch.

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An Axiomatic Approach to the Quantified Argument Calculus

Pascucci

2022

Erkenn

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Proof-Theoretic Analysis of the Quantified Argument Calculus

Cited by 9 publications

References 6 publications

Free Logic and the Quantified Argument Calculus

Free Logic and the Quantified Argument Calculus

A More Unified Approach to Free Logics

An Axiomatic Approach to the Quantified Argument Calculus

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