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Formalisations of Many‐Valued Propositional Calculi with Variable Functors
Author(s) -
Jones John
Publication year - 1985
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19850312504
Subject(s) - functor , propositional calculus , axiom , variable (mathematics) , mathematics , citation , calculus (dental) , computer science , propositional variable , artificial intelligence , mathematical economics , algebra over a field , discrete mathematics , library science , pure mathematics , intermediate logic , description logic , medicine , mathematical analysis , geometry , dentistry
Let C and N be the implication and negation functors respectively of LUKASIEWICZ (see [ 7 ] ) and let T be the tertium functor of SLUPECKI (for m = 3 see [25] , for 3 i m < N~ see [ 2 2 ] ) . Let 6, = { F , , . . ., Fk} (k 2 2 ) be a set of n-argument functors (?L 2 2 ) and let G, , . . ., G, be a (possibly empty) list of the functors N and T with no repetitions. We consider here the m-(2 5 m < N ~ ) and valued propositional calculi in which the primitive symbols are propositional variables, the constant functors G I , . . . , G, (T is not relevant in the No-valued case, of course) and variable functors taking values from the set €,. For examples of such propositional calculi which satisfy definability conditions to be given in $ 1 we give complete formalisations (see $9 2 , 3). The methods we describe were developed in the special case of variable functors taking values from the set (C, C’} (see [4], [ 5 ] ) and having N as an additional primitive constant functor (see [6]). The only designated truth value is 1.