Universal Algebra and Logic

Fall 2019 Seminars

Time: Monday, September 16, 4:10 PM
Place: SC 1312
Speaker: Adam Přenosil
Title: Glivenko theorems and semisimple companions
Abstract: The Glivenko theorem connecting intuitionistic and classical logic by means of a double negation translation, as well as its analogues connecting the modal logic S4 with S5 and the fuzzy logic BL with Lukasiewicz logic, will be shown to be instances of a general phenomenon where a logic with a well-behaved negation displays a Glivenko-like connection to what we call its semisimple companion.

 

Time: Monday, September 9, 4:10 PM
Place: SC 1312
Speaker: Adam Přenosil
Title: Semisimplicity and the excluded middle (continued)
Abstract: I will present some recent joint research with Tomáš Lávička concerning the logical interpretation of semisimplicity. We shall see that, under some mild assumptions, a quasivariety (or a logic) is semisimple if and only if it enjoys a certain general form of the law of the excluded middle. We then apply this general result to provide a simple proof of the result of Kowalski that a variety of FLew-algebras (i.e. bounded commutative integral residuated lattices) is semisimple if and only if it validates the equation 1 = x v ~(x^n) for some n. In addition to being brief and purely syntactic, our proof also has the virtue of immediately extending to varieties of bounded commutative residuated lattices without any additional work.


Time: Monday, August 26, 4:10 PM
Place: SC 1312
Speaker: Adam Přenosil
Title: Semisimplicity and the excluded middle
Abstract: I will present some recent joint research with Tomáš Lávička concerning the logical interpretation of semisimplicity. We shall see that, under some mild assumptions, a quasivariety (or a logic) is semisimple if and only if it enjoys a certain general form of the law of the excluded middle. We then apply this general result to provide a simple proof of the result of Kowalski that a variety of FLew-algebras (i.e. bounded commutative integral residuated lattices) is semisimple if and only if it validates the equation 1 = x v ~(x^n) for some n. In addition to being brief and purely syntactic, our proof also has the virtue of immediately extending to varieties of bounded commutative residuated lattices without any additional work.

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Vanderbilt University
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