Constructing Natural Extensions of Propositional Logics

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00459809" target="_blank" >RIV/67985807:_____/16:00459809 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11225-016-9671-2" target="_blank" >http://dx.doi.org/10.1007/s11225-016-9671-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-016-9671-2" target="_blank" >10.1007/s11225-016-9671-2</a>

Result language
angličtina
Original language name
Constructing Natural Extensions of Propositional Logics
Original language description
The proofs of some results of abstract algebraic logic, in particular of the transfer principle of Czelakowski, assume the existence of so-called natural extensions of a logic by a set of new variables. Various constructions of natural extensions, claimed to be equivalent, may be found in the literature. In particular, these include a syntactic construction due to Shoesmith and Smiley and a related construction due to Lo´s and Suszko. However, it was recently observed by Cintula and Noguera that both of these constructions fail in the sense that they do not necessarily yield a logic. Here we show that whenever the Lo´s–Suszko construction yields a logic, so does the Shoesmith–Smiley construction, but not vice versa. We also describe the smallest and the largest conservative extension of a logic by a set of new variables and show that contrary to some previous claims in the literature, a logic of cardinality K may have more than one conservative extension of cardinality K by a set of new variables. In this connection we then correct a mistake in the formulation of a theorem of Dellunde and Jansana.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA13-14654S" target="_blank" >GA13-14654S: An Order-Based Approach to Non-Classical Propositional and Predicate Logics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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