Polyvalued logic

by Åke Persson, Lund


By using of quantity relations it is possible to describe the properties of many basic logical concepts, as connectives, quantifiers, modalities etc. This provides a high precision tool to analyze logical contexts and logical systems. The logicists idea of a close connection between logic and math is here explicite demonstrated, but the idea to use logic to build up math has here reversed direction - propositional logic built from math. As the logic is not a proposed logic but a logic derived from the logic of quantities, it follows our intuitive everydays logic quite close for a wide range of contexts - how wide, still remains to discover.

 
Polyvalued logic is a logic derived from the logic of quantity relations and the idea of context dependent value space of quantities in the range [0,1]. It can be seen as a "boolean algebra" for truth values between 0 and 1, but not as any new "fuzzy logic" technique, as there are no fuzzy values or fuzzy sets. In this logic the differences between 'factual' and 'necessary' truth easily can be handled. The logic works unchanged directly on probabilities, and it is possibe to combine values from several truth concepts. The logic provides also a new and true conditional implication that avoid the paradoxes of implication.

First order quantity relation logic. Also the properties of several quantifiers can easily be described and handled by quantity relation logic. Syllogisms can be proved valid or not as well as reasoning by many kind of quantifiers. This logic provides also here the same conditional implication concept as in PVL that avoid many paradoxes of standard FOL.

An other quantity relation logic is Baysian logic, a logic for probabiliteis.The polyvalued logic applied to probabilistic contexts is basicly identical to baysian logic..

The pages on this site are not (yet) any complete work-thru of the logics, but rather a collection of various writings about and around quantity relation logic and it's concepts. For all pages I apologize for my bad english, and looks forward to the day when somebody creates literature of it.


HIGH LIGHTS:
Polyvalued Logic:
  • quite close to our intuitive everyday logic
  • free from paradoxes of implication
  • solves Hempel's paradox
  • easy handle of modal concepts
  • possible to combine truth values and probabilities
  • very suitable for computer implementations
First Order Quantity Relation Logic:
  • quite close to our intuitive everyday logic
  • possible to express and handle a wide range of quantifiers
  • syllogisms easy to prove
  • very suitable for computer implementations
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