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  1. Matrix-based logic for application in physics.Paul Weingartner - 2009 - Review of Symbolic Logic 2 (1):132-163.
    The paper offers a matrix-based logic (relevant matrix quantum physics) for propositions which seems suitable as an underlying logic for empirical sciences and especially for quantum physics. This logic is motivated by two criteria which serve to clean derivations of classical logic from superfluous redundancies and uninformative complexities. It distinguishes those valid derivations (inferences) of classical logic which contain superfluous redundancies and complexities and are in this sense from those which are or in the sense of allowing only the most (...)
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  • Matrix- based logic for avoiding paradoxes and its paraconsistent alternative.Paul Weingartner - 2011 - Manuscrito 34 (1):365-388.
    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 . 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 ).
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  • Basis Logic for Application in Physics and Its Intuitionistic Alternative.Paul Weingartner - 2010 - Foundations of Physics 40 (9-10):1578-1596.
    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 (...)
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  • A predicate calculus for intensional logic.Paul Weingartner - 1973 - Journal of Philosophical Logic 2 (2):220 - 303.
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  • An Alternative Propositional Calculus for Application to Empirical Sciences.Paul Weingartner - 2010 - Studia Logica 95 (1-2):233 - 257.
    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 (...)
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