Reasons from Science for Limiting Classical Logic

Weingartner, Paul

doi:10.1007/978-3-662-05679-0_15

Cited by 4 publications

(7 citation statements)

References 6 publications

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“…The reason is that RMQ contains the whole CPC as at least classically valid, that is materially valid. See principles 5,12,15,17,19,21, 24 of Sect. 4.1.…”

Section: Resultsmentioning

confidence: 99%

“…Hypothesis syllogism (transitivity of → ) (14)- (21) shows that strict validity in RMQ interprets a negation before parenthesis of a compound wff as weaker than the negation which is applied immediately to the wff. This coincides partially with intuitionistic logic, such that Principles (18)-(21) hold only materially in RMQ.…”

Section: Basic Theorems Of Cpc Which Are Strictly (Or Necessarily) Vamentioning

confidence: 99%

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Basis Logic for Application in Physics and Its Intuitionistic Alternative

Weingartner

2010

Found Phys

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This article proposes a basic logic for application in physics dispensing with the Principle of Excluded Middle. It is based on the article "Matrix Based Logics for Application in Physics (RMQ) which appeared 2009. In his article with Stachow on the Principle of Excluded Middle in Quantum Logic (QL), Peter Mittelstaedt showed that for some suitable QLs, including their own, the Principle of Excluded Middle can be added without any harm for QL; where 'without any harm for QL' means that the basic desiderata and the basic results (theorems) of those QLs remain satised in the sense that they avoid the well known difficulties with commensurability and distributivity.In the following article I want to show that the basic desiderata and results (theorems) of RMQ (of avoiding the well-known difficulties with commensurability, distributivity, fusion and Bell's inequalities) remain satised if by introducing a strong negation (or strong negation and disjunction) the resulting weak intuitionist system RMQI dispenses with the Principle of Excluded Middle; it becomes either invalid or not strictly valid.

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“…The reason is that RMQ contains the whole CPC as at least classically valid, that is materially valid. See principles 5,12,15,17,19,21, 24 of Sect. 4.1.…”

Section: Resultsmentioning

confidence: 99%

Section: Basic Theorems Of Cpc Which Are Strictly (Or Necessarily) Vamentioning

confidence: 99%

Basis Logic for Application in Physics and Its Intuitionistic Alternative

Weingartner

2010

Found Phys

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“…33 Mittelstaedt [16], Stachow [26]. 34 Cf. Pavicic-Megill [18] (14) and (16) of section 4.4 and A10 above).…”

Section: Comparison Of Rmq To Systems Of Qlmentioning

confidence: 98%

“…It derives from a similar 6-valued matrix-calculus. 34 Although both systems do not have strong necessitation (i.e. if p, then Lp) the system SS 1M contains all theorems of CPC as strictly (necessarily) valid, whereas RMQ allows as strictly valid only those theorems of CPC which (approximately) satisfy the criteria RC and RD (for avoiding the well-known difficulties), yet including all the important traditional principles of CPC.…”

Section: The Modal Logic Contained In Rmqmentioning

confidence: 99%

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An Alternative Propositional Calculus for Application to Empirical Sciences

Weingartner

2010

Stud Logica

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The purpose of the paper is to show that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. This kind of cleaning of CL has been done successfully by distinguishing two types of theorems of CL by two criteria. One criterion (RC) forbids such theorems in which parts of the consequent (conclusion) can be replaced by arbitrary parts salva validitate of the theorem. The other (RD) reduces the consequences to simplest conjunctive consequence elements. Since the application of RC and RD to CL leads to a logic without the usual closure conditions, an approximation to RC and RD has been constructed by a basic logic with the help of finite (6-valued) matrices. This basic logic called RMQ (relevance, matrix, Quantum Physics) is consistent and decidable. It distinguishes two types of validity (strict validity) and classical or material validity. All theorems of CL (here: classical propositional calculus CPC) are classically or materially valid in RMQ. But those theorems of CPC which obey RC and RD and avoid the difficulties in the application to empirical sciences and to Quantum Physics are separated as strictly valid in RMQ. In the application to empirical sciences in general the proposed logic avoids the well known paradoxes in the area of explanation, confirmation, versimilitude and Deontic Logic. Concerning the application to physics it avoids also the difficulties with distributivity, commensurability and with Bell's inequalities.

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Deontic Logic in Computer Science

Gabbay

Meyden²,

Torre³

2008

Lecture Notes in Computer Science

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The ESSLLI course material has been compiled by Leon van der Torre and Jörg Hansen. Unless otherwise mentioned, the copyright lies with the individual authors of the material. Leon van der Torre and Jörg Hansen declare that they have obtained all necessary permissions for the distribution of this material. ESSLLI 2008 and its organizers take no legal responsibility for the contents of this booklet.

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Reasons from Science for Limiting Classical Logic

Cited by 4 publications

References 6 publications

Basis Logic for Application in Physics and Its Intuitionistic Alternative

Basis Logic for Application in Physics and Its Intuitionistic Alternative

An Alternative Propositional Calculus for Application to Empirical Sciences

Deontic Logic in Computer Science

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