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Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics
Bulletin of the Section of Logic, Tome 47 (2018) no. 2
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This work adapts techniques and results first developed by Malinowski and by Marek in the context of referential semantics of sentential logics to the context of logics formalized as π-institutions. More precisely, the notion of a pseudoreferential matrix system is introduced and it is shown how this construct generalizes that of a referential matrix system. It is then shown that every π–institution has a pseudo-referential matrix system semantics. This contrasts with referential matrix system semantics which is only available for self-extensional π-institutions by a previous result of the author obtained as an extension of a classical result of Wójcicki. Finally, it is shown that it is possible to replace an arbitrary pseudoreferential matrix system semantics by a discrete pseudo-referential matrix system semantics.
Keywords: Referential Logics, Selfextensional Logics, Referential Semantics, Referential π-institutions, Selfextensional π-institutions, Pseudo- Referential Semantics, Discrete Referential Semantics 
@article{BSL_2018_47_2_a0,
     author = {Voutsadakis, George},
     title = {Categorical {Abstract} {Algebraic} {Logic:} {Pseudo-Referential} {Matrix} {System} {Semantics}},
     journal = {Bulletin of the Section of Logic},
     year = {2018},
     volume = {47},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2018_47_2_a0/}
}
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Voutsadakis, George. Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics. Bulletin of the Section of Logic, Tome 47 (2018) no. 2. http://geodesic.mathdoc.fr/item/BSL_2018_47_2_a0/