Modal logics with two kinds of necessity and possibility.

2010

Found Phys

Self Cite

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.

“…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: The Basic Logic Rmqmentioning

confidence: 99%

Basis Logic for Application in Physics and Its Intuitionistic Alternative

2010

Found Phys

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“…matrices of ∨ and →, but agrees on ¬, ∧ and modalities has been published as Weingartner (1968). This modal logic contains all theorems of CL in such a way that they hold necessarily (i.e., with cv = 2).…”

Section: Conjunction and Implicationmentioning

confidence: 99%

Matrix- based logic for avoiding paradoxes and its paraconsistent alternative

2011

Manuscrito

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The present article shows that there are consistent and decidable manyvalued systems of propositional logic which satisfy two or all the three criteria for non-trivial inconsistent theories by da Costa (1974). The weaker one of these paraconsistent system is also able to avoid a series of paradoxes which come up when classical logic is applied to empirical sciences. These paraconsistent systems are based on a 6-valued system of propositional logic for avoiding difficulties in several domains of empirical science (Weingartner (2009)).

“…matrices of ∨ and →, but agrees on ¬, ∧ and modalities has been published as[28]. This Modal Logic contains all theorems of CL in such a way that they hold necessarily (i.e.…”

mentioning

confidence: 99%

An Alternative Propositional Calculus for Application to Empirical Sciences

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.