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The
seminar is held in hybrid
format, in person (Múzeum
krt. 4/i Room 224) and
online at the following
link:
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| 6
March (Friday)
4:15 PM Room 224 +
ONLINE |
Mátyás
Lagos
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Department
of Logic, Institute of
Philosophy,
Eötvös Loránd University,
Budapest
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| Generalization
via Aggregation: An
Analogical Inference
Mechanism for Natural
Language Syntax
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How do speakers of a language
infer the grammatical structure
of a newly heard sentence? In
exemplar-based theories of
language, this inference process
is said to consist of comparing
the novel sentence to sentences
that the speaker has already
heard, and making analogical
generalizations from the
observed partial similarities.
There have been attempts at
fully specifying and
computationally implementing
such a process, but it remains
an open question whether this is
a feasible approach, given the
fact that even relatively short
word sequences tend to occur
very infrequently in corpora. In
this talk, I propose a novel
exemplar-based grammatical
inference mechanism and present
some experiments testing its
feasibility.
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| 13
March (Friday) 4:15
PM Room 224 + ONLINE
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Hongkai
Yin
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Central
European University, Vienna
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| The
Guarded Fluted Fragment of
First-Order Logic
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The
guarded fluted fragment is
the intersection of the
guarded fragment and the
fluted fragment of
first-order logic. In
this talk I showcase
a model construction
technique which turns each
first-order structure into
a modal structure and
back. Based on that, I
introduce a translation of
the guarded fluted
fragment to the basic
modal logic extended with
the universal modality,
providing a simulation of
the fragment as well as a
new proof of the
ExpTime-completeness of
the satisfiability
problem. Moreover, the
technique induces a
variant of the
unraveling construction.
As an application of the
unraveling, I show that
the analog of the
Łoś-Tarski Preservation
Theorem holds
in the fragment.
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| 20
March (Friday) 4:15
PM Room 224 + ONLINE
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| Tibor
Papp
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Eötvös
Loránd University, Department
of Logic
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| Introduction
to Universal Logic
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The first part of my doctoral
thesis is a self-developed
metalogical theory, called
Universal Logic (UL). The
doctoral thesis outlines UL as
follows:
There is a hidden internal
architecture of logic that is
obscured by the implicit
paradigms governing syntax,
semantics, and consequence. By
explicating and reformulating
these paradigms in two
distinct directions, this
hidden architecture becomes
visible.
First, modern (post-Fregean)
logic has typically approached
traditional (pre-Fregean)
logic by reformulating its
categories within modern
logical frameworks. To make
the internal architecture of
logic visible, however, this
direction must be reversed:
modern logic must be
reconstructed on the basis of
the categorical distinctions
already present in traditional
logic.
Second, the internal
architecture of logic has
typically been sought through
its algebraisation. Yet
algebraic abstraction, while
structurally powerful,
necessarily suppresses certain
features specific to logical
construction, and therefore
cannot render the full
internal architecture of logic
visible. To make this
architecture fully explicit,
it is not logic that must be
algebraised, but algebra that
must be logified.
As a result of this
reformulation, the
completeness theorem emerges
in a new light. It is a
universal property of the
internal architecture of logic
itself, rather than a result
tied to particular logical
calculi, and it can be
formally proved within the new
paradigms that make this
architecture explicit. In
other words, the absence of a
completeness theorem in
higher-order logics does not
reflect an intrinsic
limitation of logic itself; it
reveals instead that the
implicit paradigms governing
syntax, semantics, and
consequence are insufficient
to support completeness in
higher orders.
Of course, I cannot present the
entire UL during the seminar
lecture, as it is a mathematical
construction of over 100 pages.
The aim of the lecture is to
show the basic ideas on which UL
is based.
Finally, an important note: I
will give the lecture in Hungarian.
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| 27
March (Friday) 4:15
PM Room 224 + ONLINE
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Domonkos
Inges
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Eötvös
Loránd University, Department
of Logic
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| About
the distinguishing of S(Kn) and
the usage of distinguishing
coloring in cryptographic
protocols
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In this thesis, we consider
a way of breaking a graph's
symmetry: distinguishing
colorings. A distinguishing
coloring c of G colors
the vertices of G so
that the only automorphism of
the colored graph (G,c)
is the identity map. The
distinguishing number of G,
D(G), is the minimum
number of colors needed to
create a distinguishing
coloring of G. The
cost number of G, ρ(G), is
the size of the minimum color
class of an optimal
distinguishing coloring of G.
We provide the following
result for the complete graph
and its subdivision
graph: ρ(S(Kn))=ρ'(Kn),
where ρ'(G) is
the cost number of a
distinguishing edge coloring
of G.
Furthermore, we present the
known complexity of the
language DIST = {(G,k) :
D(G) ≤ k}. We
explore a research area by
giving a sketch of a
zero-knowledge protocol for
someone to commit to a
distinguishing coloring on a
graph.
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