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BEGIN:VEVENT
SUMMARY:Sándor Jenei (University of Pécs)
DTSTART;VALUE=DATE-TIME:20210108T170000Z
DTEND;VALUE=DATE-TIME:20210108T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/1
DESCRIPTION:Title:
A representation theorem for odd and even involutive commutative residuate
d chains by direct systems of abelian o-groups\nby Sándor Jenei (Univ
ersity of Pécs) as part of Nonclassical Logic Webinar\n\n\nAbstract\nAlge
braic investigations into substructural logics have been flourishing in th
e past decades\, but the focus of this research has been fairly biased tow
ards integral or idempotent or divisible structures which were already wel
l-understood. On the contrary\, (quasi)varieties of not necessarily integr
al and not necessarily divisible algebras form equivalent algebraic semant
ics for all the main logics in the linear and in the relevant family\, inc
luding Abelian logic\, and it is precisely in this area where it is possib
le to find very interesting connections with (lattice ordered) groups and
thus with classical algebra.\nIn this talk we address the problem of struc
tural description of involutive commutative residuated lattices\, the non-
integral case. The algebras in our focus are non-divisible and non-idempot
ent either. Related attempts in the literature have\, so far\, been confin
ed to either lattice-ordered groups (the cancellative case) or Sugihara mo
noids (the idempotent case). For all involutive commutative residuated cha
ins\, where either the residual complement operation leaves the unit eleme
nt fixed (odd case) or the unit element is the cover of its residual compl
ement (even case)\, a representation theorem will be presented in this tal
k by means of direct systems of abelian o-groups.\n
LOCATION:https://researchseminars.org/talk/NCLogic/1/
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BEGIN:VEVENT
SUMMARY:Vincenzo Marra (University of Milan)
DTSTART;VALUE=DATE-TIME:20210115T170000Z
DTEND;VALUE=DATE-TIME:20210115T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/2
DESCRIPTION:Title:
Remarks on logics for probability\, with an eye toward universal construct
ions (Part II)\nby Vincenzo Marra (University of Milan) as part of Non
classical Logic Webinar\n\n\nAbstract\nThe use of logic to reason about pr
obability has a long tradition in science\, and any ambition of surveying
past work in a single talk would be ill-advised. Instead\, in this light\,
informal\, leisurely talk\, I attempt to highlight selected fundamental i
ssues that arise in the field. For example\, starting from the logical sid
e: Is "The coin probably lands heads" a sentence in classical logic? Or is
it a modal sentence? Can we attach any meaning to the sentence "It is lik
ely that the coin probably lands heads"? And how do we infer one such sent
ence from another? By the end of the talk\, I hope to manage to indicate t
hat convincing answers to these and other related questions are available.
These answers pertain to logic and algebra\, but in turn suggest new ques
tions in probability theory that are not traditionally associated with tha
t field\; for example\, is there a "free"\, or most general\, assignment o
f probabilities to the sentence "The coin lands heads”?\n
LOCATION:https://researchseminars.org/talk/NCLogic/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Flaminio (IIIA-CSIC)
DTSTART;VALUE=DATE-TIME:20210122T170000Z
DTEND;VALUE=DATE-TIME:20210122T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/3
DESCRIPTION:Title:
Probability logic on many-valued events: standard completeness and (a kind
of) algebraic semantics\nby Tommaso Flaminio (IIIA-CSIC) as part of N
onclassical Logic Webinar\n\n\nAbstract\nProving 'standard completeness'\,
that is completeness with respect to a class of algebras based on the rea
l unit interval\, has been for a long time a central problem for t-norm ba
sed (fuzzy) logics. Elaborated techniques to prove this kind of result hav
e been developed and most of them rely on the fact that totally ordered al
gebras can be embedded\, or just partially embedded\, into standard struct
ures. However\, when we move from t-norm based logics to probabilistic mod
al logics based on them\, these methods are no longer applicable and it is
necessary to consider new ideas to prove standard completeness. In this s
eminar\, besides clarifying what ’standard completeness’ means in the
probabilistic setting\, we will present the logic FP(L\, L)\, a formalisms
that allows to reason about probabilistic statements on events represente
d as formulas of Lukasiewicz logic\, and we prove it to be standard comple
te. Further elaborating on the standard completeness for FP(L\, L) we will
also present results from an ongoing research line that allow to regard a
peculiar class of projective MV-algebras as a semantics for that probabil
ity logic.\n
LOCATION:https://researchseminars.org/talk/NCLogic/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Bianchi
DTSTART;VALUE=DATE-TIME:20210129T170000Z
DTEND;VALUE=DATE-TIME:20210129T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/4
DESCRIPTION:Title:
Strictly join irreducible varieties of BL-algebras\nby Matteo Bianchi
as part of Nonclassical Logic Webinar\n\n\nAbstract\nBasic Logic BL\, intr
oduced by P. Hajek in 1998\, is the logic of all continuous t-norms and th
eir residua. The variety of BL-algebras forms the algebraic semantics of B
L.\nLet V be a variety of BL-algebras\, and let L(V) be its lattice of sub
varieties\, ordered by inclusion.\nV is called strictly join irreducible (
SJI) if\, whenever V is the join of a non-empty set S of varieties of BL-a
lgebras\, then V belongs to S.\nEvery variety in L(V) is obtained as join
of SJI varieties\, which may be considered as the building blocks of all t
he varieties in L(V). In this talk I will present the results of a recent
joint work with Stefano Aguzzoli\, where we provided a full classification
of the SJI varieties of BL-algebras.\n
LOCATION:https://researchseminars.org/talk/NCLogic/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sándor Jenei (University of Pécs)
DTSTART;VALUE=DATE-TIME:20210205T170000Z
DTEND;VALUE=DATE-TIME:20210205T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/5
DESCRIPTION:Title:
Amalgamation in classes of involutive commutative residuated lattices\
nby Sándor Jenei (University of Pécs) as part of Nonclassical Logic Webi
nar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NCLogic/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tadeusz Litak (Friedrich-Alexander-University of Erlangen-Nürnber
g)
DTSTART;VALUE=DATE-TIME:20210212T170000Z
DTEND;VALUE=DATE-TIME:20210212T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/7
DESCRIPTION:Title:
Lewis meets Brouwer\, or perhaps Heyting\nby Tadeusz Litak (Friedrich-
Alexander-University of Erlangen-Nürnberg) as part of Nonclassical Logic
Webinar\n\n\nAbstract\nThis talk is an introduction to what one might call
the Heyting-Lewis calculus of strict implication over the intuitionistic
propositional base\; the names "constructive strict implication" or "Brouw
er-Lewis implication/calculus" have also been used. The corresponding clas
s of algebras can be seen as the fusion of Heyting algebras and weak Heyti
ng algebras (Celani and Jansana) over the shared bounded lattice reduct. (
Super)intuitionistic modal logics with unary box are a limiting case\, but
in the intuitionistic setting there are many examples where strict implic
ation is not reducible to box. Its variants arise\, e.g.\, in the context
of preservativity in Heyting Arithmetic (where it was first invented by Vi
sser)\, in the inhabitation logic of simple type theory extended with Hask
ell-style arrows\, and in a generalization of Intuitionistic Epistemic Log
ic of Artemov and Protopopescu. The move to the intuitionistic propositio
nal base also throws interesting light on the complex fate of Lewis' origi
nal systems. The Heyting-Lewis calculus enjoys a natural Kripke semantics
(first studied by Iemhoff and coauthors)\, which also allows defining an a
ppropriate notion of descriptive frame and Esakia-style dualities. Further
more\, one can follow the Wolter-Zakharyaschev idea of generalizing the G
ödel-McKinsey-Tarski translation\, reducing the metatheory of Heyting-Lew
is logics to suitable bimodal logics over the classical propositional base
\, obtaining a suitable variant of the Blok-Esakia theorem\, and (re)provi
ng many correspondence\, completeness\, decidability and fmp results in an
uniform way. However\, it seems that ultimately one will have to drop one
of the axioms\, losing the natural Kripke semantics. In the final part of
the talk\, I am going to discuss alternative semantics for the weakened s
ystem and its position in the broader landscape of intuitionistic logics w
ith an additional implication-like connective. This talk involves joint wo
rk with Albert Visser (Utrecht University)\, Jim de Groot and Dirk Pattins
on (ANU)\, Igor Sedlar and the Prague group\, and Miriam Polzer (Google).\
n
LOCATION:https://researchseminars.org/talk/NCLogic/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Bonzio (University of Turin)
DTSTART;VALUE=DATE-TIME:20210226T170000Z
DTEND;VALUE=DATE-TIME:20210226T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/8
DESCRIPTION:by Stefano Bonzio (University of Turin) as part of Nonclassica
l Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NCLogic/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Pra Baldi (University of Cagliari)
DTSTART;VALUE=DATE-TIME:20210305T170000Z
DTEND;VALUE=DATE-TIME:20210305T190000Z
DTSTAMP;VALUE=DATE-TIME:20210228T175355Z
UID:NCLogic/9
DESCRIPTION:Title:
On a logico-algebraic approach to AGM belief contraction theory\nby Mi
chele Pra Baldi (University of Cagliari) as part of Nonclassical Logic Web
inar\n\n\nAbstract\nIn this seminar we investigate AGM belief contraction
operators by using the tools of algebraic logic. We generalize the notion
of contraction to arbitrary finitary propositional logics\, and we show ho
w to switch from a syntactic-based approach to a semantic one. This allows
to build a solid bridge between the validity of AGM postulates in a propo
sitional logic and specific algebraic properties of its intended algebraic
counterpart. Some applications to substructural logics are provided.\n(j.
w.w. Davide Fazio)\n
LOCATION:https://researchseminars.org/talk/NCLogic/9/
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