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BEGIN:VEVENT
SUMMARY:Sándor Jenei (University of Pécs)
DTSTART:20210108T170000Z
DTEND:20210108T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/1
DESCRIPTION:Title: A representation theorem for odd and even involutive commutative re
siduated chains by direct systems of abelian o-groups\nby Sándor Jene
i (University of Pécs) as part of Nonclassical Logic Webinar\n\n\nAbstrac
t\nAlgebraic investigations into substructural logics have been flourishin
g in the past decades\, but the focus of this research has been fairly bia
sed towards integral or idempotent or divisible structures which were alre
ady well-understood. On the contrary\, (quasi)varieties of not necessarily
integral and not necessarily divisible algebras form equivalent algebraic
semantics for all the main logics in the linear and in the relevant famil
y\, including Abelian logic\, and it is precisely in this area where it is
possible to find very interesting connections with (lattice ordered) grou
ps and thus with classical algebra.\nIn this talk we address the problem o
f structural description of involutive commutative residuated lattices\, t
he non-integral case. The algebras in our focus are non-divisible and non-
idempotent either. Related attempts in the literature have\, so far\, been
confined to either lattice-ordered groups (the cancellative case) or Sugi
hara monoids (the idempotent case). For all involutive commutative residua
ted chains\, where either the residual complement operation leaves the uni
t element fixed (odd case) or the unit element is the cover of its residua
l complement (even case)\, a representation theorem will be presented in t
his talk by means of direct systems of abelian o-groups.\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Marra (University of Milan)
DTSTART:20210115T170000Z
DTEND:20210115T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/2
DESCRIPTION:Title: Remarks on logics for probability\, with an eye toward universal co
nstructions (Part II)\nby Vincenzo Marra (University of Milan) as part
of Nonclassical Logic Webinar\n\n\nAbstract\nThe use of logic to reason a
bout probability has a long tradition in science\, and any ambition of sur
veying past work in a single talk would be ill-advised. Instead\, in this
light\, informal\, leisurely talk\, I attempt to highlight selected fundam
ental issues that arise in the field. For example\, starting from the logi
cal side: 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 likely that the coin probably lands heads"? And how do we infer one su
ch sentence from another? By the end of the talk\, I hope to manage to ind
icate that convincing answers to these and other related questions are ava
ilable. These answers pertain to logic and algebra\, but in turn suggest n
ew questions in probability theory that are not traditionally associated w
ith that field\; for example\, is there a "free"\, or most general\, assig
nment of probabilities to the sentence "The coin lands heads”?\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Flaminio (IIIA-CSIC)
DTSTART:20210122T170000Z
DTEND:20210122T190000Z
DTSTAMP:20260404T111137Z
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 pa
rt of Nonclassical Logic Webinar\n\n\nAbstract\nProving 'standard complete
ness'\, that is completeness with respect to a class of algebras based on
the real unit interval\, has been for a long time a central problem for t-
norm based (fuzzy) logics. Elaborated techniques to prove this kind of res
ult have been developed and most of them rely on the fact that totally ord
ered algebras can be embedded\, or just partially embedded\, into standard
structures. However\, when we move from t-norm based logics to probabilis
tic modal logics based on them\, these methods are no longer applicable an
d it is necessary to consider new ideas to prove standard completeness. In
this seminar\, besides clarifying what ’standard completeness’ means
in the probabilistic setting\, we will present the logic FP(L\, L)\, a for
malisms that allows to reason about probabilistic statements on events rep
resented as formulas of Lukasiewicz logic\, and we prove it to be standard
complete. Further elaborating on the standard completeness for FP(L\, L)
we will also present results from an ongoing research line that allow to r
egard a peculiar class of projective MV-algebras as a semantics for that p
robability logic.\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Bianchi
DTSTART:20210129T170000Z
DTEND:20210129T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/4
DESCRIPTION:Title: Strictly join irreducible varieties of BL-algebras\nby Matteo B
ianchi as part of Nonclassical Logic Webinar\n\n\nAbstract\nBasic Logic BL
\, introduced by P. Hajek in 1998\, is the logic of all continuous t-norms
and their residua. The variety of BL-algebras forms the algebraic semanti
cs of BL.\nLet V be a variety of BL-algebras\, and let L(V) be its lattice
of subvarieties\, ordered by inclusion.\nV is called strictly join irredu
cible (SJI) if\, whenever V is the join of a non-empty set S of varieties
of BL-algebras\, then V belongs to S.\nEvery variety in L(V) is obtained a
s join of SJI varieties\, which may be considered as the building blocks o
f all the 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 classif
ication of the SJI varieties of BL-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sándor Jenei (University of Pécs)
DTSTART:20210205T170000Z
DTEND:20210205T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/5
DESCRIPTION:Title: Amalgamation in classes of involutive commutative residuated lattic
es\nby Sándor Jenei (University of Pécs) as part of Nonclassical Log
ic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tadeusz Litak (Friedrich-Alexander-University of Erlangen-Nürnber
g)
DTSTART:20210212T170000Z
DTEND:20210212T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/7
DESCRIPTION:Title: Lewis meets Brouwer\, or perhaps Heyting\nby Tadeusz Litak (Fri
edrich-Alexander-University of Erlangen-Nürnberg) as part of Nonclassical
Logic Webinar\n\n\nAbstract\nThis talk is an introduction to what one mig
ht call the Heyting-Lewis calculus of strict implication over the intuitio
nistic propositional base\; the names "constructive strict implication" or
"Brouwer-Lewis implication/calculus" have also been used. The correspondi
ng class of algebras can be seen as the fusion of Heyting algebras and wea
k Heyting algebras (Celani and Jansana) over the shared bounded lattice re
duct. (Super)intuitionistic modal logics with unary box are a limiting cas
e\, but in the intuitionistic setting there are many examples where strict
implication is not reducible to box. Its variants arise\, e.g.\, in the c
ontext of preservativity in Heyting Arithmetic (where it was first invente
d by Visser)\, in the inhabitation logic of simple type theory extended wi
th Haskell-style arrows\, and in a generalization of Intuitionistic Episte
mic Logic of Artemov and Protopopescu. The move to the intuitionistic pro
positional base also throws interesting light on the complex fate of Lewis
' original systems. The Heyting-Lewis calculus enjoys a natural Kripke sem
antics (first studied by Iemhoff and coauthors)\, which also allows defini
ng an appropriate notion of descriptive frame and Esakia-style dualities.
Furthermore\, one can follow the Wolter-Zakharyaschev idea of generalizing
the Gödel-McKinsey-Tarski translation\, reducing the metatheory of Heyti
ng-Lewis logics to suitable bimodal logics over the classical propositiona
l base\, obtaining a suitable variant of the Blok-Esakia theorem\, and (re
)proving many correspondence\, completeness\, decidability and fmp results
in an uniform way. However\, it seems that ultimately one will have to dr
op one of the axioms\, losing the natural Kripke semantics. In the final p
art of the talk\, I am going to discuss alternative semantics for the weak
ened system and its position in the broader landscape of intuitionistic lo
gics with an additional implication-like connective. This talk involves jo
int work with Albert Visser (Utrecht University)\, Jim de Groot and Dirk P
attinson (ANU)\, Igor Sedlar and the Prague group\, and Miriam Polzer (Goo
gle).\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Bonzio (University of Turin)
DTSTART:20210226T170000Z
DTEND:20210226T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/8
DESCRIPTION:by Stefano Bonzio (University of Turin) as part of Nonclassica
l Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Pra Baldi (University of Cagliari)
DTSTART:20210305T170000Z
DTEND:20210305T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/9
DESCRIPTION:Title: On a logico-algebraic approach to AGM belief contraction theory
\nby Michele Pra Baldi (University of Cagliari) as part of Nonclassical Lo
gic Webinar\n\n\nAbstract\nIn this seminar we investigate AGM belief contr
action operators by using the tools of algebraic logic. We generalize the
notion of contraction to arbitrary finitary propositional logics\, and we
show how 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 propositional logic and specific algebraic properties of its intended al
gebraic counterpart. Some applications to substructural logics are provide
d.\n(j.w.w. Davide Fazio)\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serafina Lapenta (University of Salerno)
DTSTART:20210312T170000Z
DTEND:20210312T190000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/10
DESCRIPTION:Title: Tackling the Pierce-Birkhoff conjecture via logic\nby Serafina
Lapenta (University of Salerno) as part of Nonclassical Logic Webinar\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Bianchi
DTSTART:20210319T160000Z
DTEND:20210319T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/11
DESCRIPTION:Title: On linear varieties of MTL-algebras\nby Matteo Bianchi as part
of Nonclassical Logic Webinar\n\n\nAbstract\nA variety of MTL-algebras is
called linear whenever its lattice of subvarieties\, ordered by inclusion
\, is linearly ordered. In this talk we will describe some properties of t
he linear varieties of MTL-algebras\, and we will provide a full classific
ation of the linear varieties of BL-algebras and WNM-algebras. We will als
o discuss some additional topics and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tadeusz Litak (Friedrich-Alexander-University of Erlangen-Nürnber
g)
DTSTART:20210326T160000Z
DTEND:20210326T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/13
DESCRIPTION:by Tadeusz Litak (Friedrich-Alexander-University of Erlangen-N
ürnberg) as part of Nonclassical Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shay Logan (Kansas State University)
DTSTART:20210423T160000Z
DTEND:20210423T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/14
DESCRIPTION:by Shay Logan (Kansas State University) as part of Nonclassica
l Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Vetterlein (JKU Linz)
DTSTART:20210416T160000Z
DTEND:20210416T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/15
DESCRIPTION:Title: Orthogonality spaces\, ortholattices\, and inner-product spaces\nby Thomas Vetterlein (JKU Linz) as part of Nonclassical Logic Webinar\n
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Carnielli (University of Campinas)
DTSTART:20210430T160000Z
DTEND:20210430T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/16
DESCRIPTION:Title: Paraconsistent Possibilistic Logics\nby Walter Carnielli (Univ
ersity of Campinas) as part of Nonclassical Logic Webinar\n\n\nAbstract\nI
intend to explain the possibility and necessity models based\non theL
ogics of Formal Inconsistency (LFI's)\, which we call `credal\ncalculi'\,
taking advantage of their expressivity in terms of the\nnotions of cons
istency and inconsistency. Some basic properties of\npossibility and nec
essity\nfunctions over LFI's are provided. A nice aspect of this talk
is\nhow logic can be connected to the treatment of information\, and I
\ndiscuss some examples showing how such logics\nattain realistic models
for artificial judgement. This is a joint\nwork with Juliana Bueno-Sole
r.\n\nReference:\n\nW. A. Carnielli and J. Bueno-Soler. Credal Calculi\
, Evidence\, and\nConsistency. Outstanding Contributions to Logic\, edit
ed by O. Arieli\nand A. Zamansky\, Springer\, 2021\, in print.\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Moraschini (University of Barcelona)
DTSTART:20210507T160000Z
DTEND:20210507T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/17
DESCRIPTION:by Tommaso Moraschini (University of Barcelona) as part of Non
classical Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sedlár (Czech Academy of Sciences)
DTSTART:20210528T160000Z
DTEND:20210528T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/18
DESCRIPTION:by Igor Sedlár (Czech Academy of Sciences) as part of Nonclas
sical Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Cintula (Czech Academy of Sciences)
DTSTART:20210604T160000Z
DTEND:20210604T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/19
DESCRIPTION:by Petr Cintula (Czech Academy of Sciences) as part of Nonclas
sical Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Bílková (Czech Academy of Sciences)
DTSTART:20210618T160000Z
DTEND:20210618T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/21
DESCRIPTION:by Marta Bílková (Czech Academy of Sciences) as part of Nonc
lassical Logic Webinar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Abbadini (University of Salerno)
DTSTART:20210521T160000Z
DTEND:20210521T180000Z
DTSTAMP:20260404T111137Z
UID:NCLogic/22
DESCRIPTION:Title: Is the category of locally finite MV-algebras equivalent to an equ
ational class?\nby Marco Abbadini (University of Salerno) as part of N
onclassical Logic Webinar\n\n\nAbstract\nLocally finite MV-algebras form a
subclass of MV-algebras which is closed under homomorphic images\, subalg
ebras\, and finite products\, but not under arbitrary ones. However\, the
category of locally finite MV-algebras with homomorphisms has arbitrary pr
oducts in the classical categorical sense. Driven by these considerations\
, D. Mundici posed the following question:\nIs the category of locally fin
ite MV-algebras equivalent to an equational class? (D. Mundici. Advanced
Lukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011\, p. 235\, pr
oblem 3.)\n\nWe answer this question. \n\nOur proofs rest upon the duality
between locally finite MV-algebras and multisets established by R. Cignol
i\, E. J. Dubuc\, and D. Mundici\, and categorical characterizations of va
rieties established by J. Duskin\, F. W. Lawvere\, and others.\n
LOCATION:https://stable.researchseminars.org/talk/NCLogic/22/
END:VEVENT
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