This symposium celebrates the 60th birthday of Professor Lauri Hella. During
his career, Lauri has worked on a range of topics in mathematical logic. He has
especially concentrated on finite model theory, where his interests include, e.g.,
descriptive complexity and generalized quantifiers. His recent work also includes
contributions to dependence logic and its variants.
The symposium will feature invited talks by many of Lauri's friends and collaborators, including:

Title 
Miguel Couceiro 
On the Efficiency of Normal Form Systems for Representing Boolean Functions
The motivation for this talk will take us back to my doctoral work
under the supervision of Stephan Foldes and Lauri Hella. One of the many topics
that were investigated was normal form systems for representing Boolean functions.
There are several was to formalize this intuitive notion of normal form system (NFS).
Our first proposal was essentially to consider (NFS) of Boolean functions as
factorizations of the class of all Boolean functions into a composition of clones.
This formalism enabled a preordering of NFSs that led to a classification of NFSs.
In particular, it shows that the median NFS (that uses a single nontrivial connective,
the ternary median or majority function) is more "efficient" than classical CNF, DNF and
the polynomial NFSs. However, this formalism failed to take into account other natural NFSs
nor to structural properties of terms and connectives.
Recently, we revisited this topic with my doctoral student Pierre Mercuriali and
reconsidered NFSs as being sets of stratified terms over a fixed set of term connectives.
For a fixed NFS A, the complexity of a Boolean function f with respect to A is the
minimum of the sizes of terms in A that represent f. This induces a preordering of NFSs
that includes the latter one: an NFS A is polynomially as efficient as an NFS B if
there is a polynomial P with integer coefficients such that the complexity of any Boolean function
f with respect to A is at most the value of P in the complexity of f with respect to B.
In this talk we will describe those NFSs that are optimal, i.e., that are minimal with respect to
the latter preorder, and we will show that these minimal NFSs are all polynomially equivalent to
the median NFS. Moreover, we will address some natural questions, e.g.:
Does optimality depend on the arity of connectives?
Does it depend on the number of connectives used?
We will provide (perhaps surprising) answers to these questions and, if time allows,
we will discuss the complexity of some inherent problems such as that of finding
minimal representations for a given optimal NFS.
The results presented were obtained in joint works with S. Foldes, E. Lehtonen, P. Mercuriali,
R. Péchoux and A. Saffidine.
Talk (pdf)

Anuj Dawar 
Symmetric Circuits with nonSymmetric Gates
Formulas in logic, defining properties of finite structures, can be
translated to families of circuits which satisfy a natural symmetry
condition. In joint work with Matt Anderson I showed that the
expressive power of fixedpoint logic with counting is exactly
characterized by polynommiallyuniform families of symmetric circuits in
a basis of gates including the Boolean functions and majority functions.
The technical proofs rely heavily on the fact that the Boolean
functions and the majority function are all *symmetric* functions in the
sense of being invariant to all permutations of the input. In this talk
I consider extensions with gates that are not necessarily symmetric and
show how to relate them to logics with operators (such as generalized
quantifiers) which define the corresponding operations.
This is joint work with Gregory Wilsenach.
Talk (pdf)

Valentin Goranko 
Playing with time and playing in time
I will present gametheoretic semantics (GTS) for the branching time temporal logic CTL. I will compare that
semantics with the traditional, compositional semantics for CTL and will show how the GTS naturally generates
alternative 'timebounded' semantics, where time limits are imposed on players to demonstrate the truth of the
formula they claim to be true. I will then discuss some aspects of CTL with the nonstandard finitelybounded
semantics and will present briefly some technical results, including complete tableaux and axiomatic system for it.
The talk is based on a joint work with Antti Kuusisto (University of Bremen) and Raine Rönnholm (University of Tampere).
Talk (pdf)

Tapani Hyttinen 
Firstorder theory of free projective planes
M. Hall introduced free projective planes
π^{n}, 4≤n≤ω, in [Ha]. In the talk,
we start by
looking at the basic concepts around these planes and then
we will discuss on the
properties of the theory of these planes
i.e. the properties of the theory that
consists of all
firstorder sentences true in every
free projective plane. This talk is based on an ongoing
research
with Gianluca Paolini.
Reference
M. Hall, Projective planes, Transactions of American Mathematical
Society, vol. 54, 1943, 229277.

Juliette Kennedy 
On Kreisel's Squeezing Argument
G. Kreisel has suggested that squeezing arguments, originally formulated for the informal concept of first order
validity, should be extendable to second order logic, although he points out obvious obstacles. We develop this
idea in the light of more recent advances and delineate the difficulties across the spectrum of extensions of
first order logics by generalised quantifiers and infinitary logics. In particular we argue that if the relevant
informal concept is read as informal in the precise sense of being untethered to a particular semantics, then the
squeezing argument goes through in the second order case. Consideration of weak forms of Kreisel's squeezing argument
leads naturally to reflection principles of set theory.

Phokion Kolaitis 
Logic, Constraints, and Quantum Information
Constraint satisfaction comprises a broad class of fundamental algorithmic problems that
are encountered across several different areas of computer science and artificial intelligence.
In 1978, Schaefer characterized the computational complexity of all constraint satisfaction problems
over the Boolean domain, a result that has become known as Schaefer's Dichotomy Theorem. We investigate
an algebraization of Schaefer's framework in which the Fourier transform is used to represent constraints
by multilinear polynomials. The polynomial representation of constraints gives rise to a relaxation of
the notion of satisfiability for constraint satisfaction problems in which the values to variables are
linear operators on some Hilbert space. For constraints given by a system of linear equations over the
twoelement field, this relaxation has received considerable attention in the foundations of quantum
information, where such constructions as Mermin's magic square show that there are systems that have
no solutions in the Boolean domain, but have solutions via operator assignments on some finitedimensional
Hilbert space. We completely characterize the classes of Boolean relations for which there is a gap between
satisfiability in the Boolean domain and the relaxation of satisfiability via operator assignments.
Our main result is established via the systematic use of primitivepositive definability and logical
reductions that preserve satisfiability gaps.
This is joint work with Albert Atserias at the Polytechnic University of Catalonia (UPC) and Simone Severini at University College London (UCL).
Talk (pdf)

Antti Kuusisto 
Model counting beyond twovariable logic
Model counting problems offer a general, logicbased approach to enumerative combinatorics.
The model counting problem of a firstorder sentence takes as input an integer ntypically given in
unaryand outputs the number of nelement models of the sentence;
the domain of the models is taken to be {0,...,n1}.
It has recently been shown that this problem is in polynomial time for all sentences of twovariable
logic. We extend this result to some relevant extensions of twovariable logic, and we also
provide a complete classification of the firstorder prefix classes according to the complexities
of the associated model counting problems.

Kerkko Luosto 
Studying quantifiers with Lauri
One of the central research fields of Finnish logicians, which has also
been quite a distinctive feature of Finnish logic, has been the study of
generalized quantifiers. I shall survey some contributions to this
field from the point of view how Lauri's ideas affected my own research,
and the research of quantifiers in general. Natural topics are thus
games of the Ehrenfeucht–Fraïssé type, quantifiers hierarchies
and definability theory of quantifiers. My survey starts from 1980's
and ends in the results of this decade; time permitting I shall discuss
the future of the quantifier theory.

Jukka Suomela 
Logical Characterisations in Distributed Computing
In early 2010, a group of logicians and computer scientists from Tampere and Helsinki joined forces and started
to explore connections between modal logic and weak models of distributed computing. Our collaboration initiated
the study of distributed computing from the perspective of descriptive complexity theory.
The field is still at its infancy, but others are already following. In 2017, Fabian Reiter defended his doctoral thesis
at Paris Diderot. To my knowledge, this is the first PhD thesis about the logical characterisations of models of distributed
computing; it builds on the foundations of the work that we did here in Finland, and extends it in new exciting directions,
far beyond what I envisioned to be possible in the near future.
In this talk I will give an overview of the development of the descriptive complexity theory for distributed computing,
and in particular on the impact this has had on our understanding of the foundations of distributed computing. I will
also explore some new ideas that arose from this line of research, such as the introduction of alternation
(cf. alternating Turing machines) in models of distributed computing.
Talk (pdf)

José María TurullTorres 
On Fragments of Higher Order Logics that on Finite Structures Collapse to a Lower Order
We define new fragments of higherorder logics of order three and above, and investigate
their expressive power over finite models. The key unifying property of these fragments
is that they all admit inexpensive algorithmic translations of their formulae to equivalent
secondorder logic formulae. That is, within these fragments we can make use of third and
higherorder quantification without paying the extremely high complexity price associated with them.
The main fragment, denoted HO^{i,P}, is defined by restricting the size of the valuating
ith (and lower) order relations for the ith order variables to be of a polynomial size w.r.t. the size of the model.
Although theoretical in nature, the results reported here are more significant from a practical perspective.
We believe that there are many examples of properties of finite models (queries from the perspective of relational
databases) which can be simply and elegantly defined by formulae of the higherorder fragments studied in this work.
For many of those properties, the equivalent secondorder formulae can be very complicated and unintuitive.
By using the same strategy, it can be shown that for every i ≥ k ≥ j ≥ 4 the fragments of
HO^{i,exp(j2)} where the size of the valuating kth order relations for the kth order variables
are restricted to be of size O(exp(j2)) w.r.t. the size of the model, collapse to HO^{j}
(we denote as exp(m) a function with a stack of m exponents 2, topped by O(n^{O(1)})).
As an example, we will briefly describe sketches of higher order formulae for some problems where the use
of an order higher than the one that corresponds to their respective complexity, makes the formulas more
intuitive and clear, and hence less likely to be incorrect.
Inprogress joint work with Flavio Ferrarotti and Senén González.
Talk (pdf)

Jonni Virtema 
Expressivity within secondorder transitiveclosure logic
Secondorder transitiveclosure logic, SO(TC), is an expressive declarative language that captures
the complexity class PSPACE. Already its monadic fragment, MSO(TC), allows the expression of various
NPhard and even PSPACEhard problems in a natural and elegant manner. As SO(TC) offers an attractive
framework for expressing properties in terms of declaratively specified computations, it is interesting
to understand the expressivity of different features of the language. In this talk we focuse on the fragment
MSO(TC), as well on the purely existential fragment SO(2TC)(E); in 2TC, the TC operator binds only tuples
of relation variables. We show that, with respect to expressive power, SO(2TC)(E) collapses to
existential firstorder logic. In addition we study the relationship of MSO(TC) to an extension of MSO(TC)
with counting features (CMSO(TC)) as well as to orderinvariant MSO. We show that the expressive powers
of CMSO(TC) and MSO(TC) coincide. Moreover we establish that, over unary vocabularies, MSO(TC) strictly
subsumes orderinvariant MSO.
This is joint work with Flavio Ferrarotti and Jan Van den Bussche.
Talk (pdf)

Jouko Väänänen 
Generalized Quantifiers
After a short review of generalized quantifiers in Tarski semantics, we turn to team semantics. Generalized quantifiers
can be introduced in team semantics in (at least) three different ways: as atoms, relative atoms (to be defined), and as
logical operations. The latter two lead to equivalent logics (at least) in the case of simply unary quantifiers. In this
way generalized quantifiers give rise to new atoms. We focus on a particular one which we call the anonymity atom.
The intuition behind this atom is the following: Suppose we have data about some individuals and the values of some
attributes are publicly known while the values of some other attributes are sensitive personal data that should be
protected from becoming public. Anonymity in this context means the impossibility to derive the values of the sensitive
attributes from the values of the publicly known attributes, and this impossibility should be true of each individual.
After introducing the anonymity atom we give axioms for it and prove an Armstrongstyle Completeness Theorem for it.

Dag Westerståhl 
Why should we care about logical constants?
Most logicians would agree that logical consequence is a central notion in logic. The dual notion of a logical constant
has received less attention: one is usually satisfied on pragmatic grounds with a standard set of logical constants and
doesn't worry much about why they are so special. Yet consequence depends on constants: as Bolzano and Tarski made precise,
every choice of a set X of constants yields a corresponding consequence relation, defined in terms of truth preservation
under replacement/reinterpretation of symbols outside X. How to choose X? Both Bolzano and Tarski emphasized the fundamental
importance of this question, and admitted they had no answer (at the time: 1837 and 1936, respectively). However, intuitions
about 'what follows from what' are stronger than those about constancy, and it makes sense to try to see how constants depend
on consequence, by 'extracting' the constants from a given consequence relation. A natural Galois connection establishes the
duality between sets of constants and Bolzano/Tarskian consequence relations.
Logical consequence relations are also defined syntactically, via rules. If such a relation coincides with Bolzano/Tarskian
semantic consequence relative to the standard logical symbols with their standard interpretation, we have soundness and
completeness: syntax matches semantics. But the other side of the coin, that semantics should match syntax in the sense
that the meaning of the logical symbols is somehow determined by the relation of logical consequence, seems just as important.
Such categoricity results were the main focus of Carnap's 1943 book The Formalization of Logic, but the topic has been rather
neglected since. I will present some recent joint work with Denis Bonnay on these issues, applied to familiar logical languages.

Note: There are some slides (click titles).
 
Program
The program of the symposium can be found
here.
Meeting place for the bus
