Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics
Bulletin of the Section of Logic (2018)
- Volume: 47, Issue: 2
- ISSN: 0138-0680
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topGeorge Voutsadakis. "Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics." Bulletin of the Section of Logic 47.2 (2018): null. <http://eudml.org/doc/295594>.
@article{GeorgeVoutsadakis2018,
abstract = {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.},
author = {George Voutsadakis},
journal = {Bulletin of the Section of Logic},
keywords = {Referential Logics; Selfextensional Logics; Referential Semantics; Referential π-institutions; Selfextensional π-institutions; Pseudo- Referential Semantics; Discrete Referential Semantics},
language = {eng},
number = {2},
pages = {null},
title = {Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics},
url = {http://eudml.org/doc/295594},
volume = {47},
year = {2018},
}
TY - JOUR
AU - George Voutsadakis
TI - Categorical Abstract Algebraic Logic: Pseudo-Referential Matrix System Semantics
JO - Bulletin of the Section of Logic
PY - 2018
VL - 47
IS - 2
SP - null
AB - 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.
LA - eng
KW - Referential Logics; Selfextensional Logics; Referential Semantics; Referential π-institutions; Selfextensional π-institutions; Pseudo- Referential Semantics; Discrete Referential Semantics
UR - http://eudml.org/doc/295594
ER -
References
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