August 7-12, 2011, Ljubljana, Slovenia
part of ESSLLI 2011
workshop is now over but ... lots of materials are still available!
Click on the title of a talk to access the materials used during
the workshop (abstracts, slides, handouts, etc.).
Denis Bonnay (Paris Ouest University)
Dag Westerståhl (University of Gothenburg)
Uli Sauerland (Zentrum für Allgemeine Sprachwissenschaft, Berlin)
All logical systems make a distinction between logical and non-logical
symbols, and the meaning of the former needs to be specified in detail
and in effect defines the logic in question. This distinction is
usually stipulated (though it can be argued that natural languages make
a similar distinction), but the issue of the grounds for it, i.e. of
what characterizes a logical constant, is a central question in logic,
cutting across the huge variety of logical systems existing today. This
question has been tackled from various sides, ranging from historical
investigation to formal criteria spelled out within different logical
frameworks. The main aim of the workshop is to gain a better
understanding of the problem by bringing together complementary
approaches coming from various fields:
*** Logic. Given a particular
logical framework (e.g. semantic, proof-theoretic, game-theoretic), is
there a systematic way to characterize the class of logical constants
within that framework? Is it possible to provide an integrated account
covering the various frameworks?
*** Philosophy of Logic and Mathematics.
What are the relevant conceptual analyses of logicality? What is the
philosophical significance of the distinction for the philosophy of
logic and philosophy of mathematics, e.g. regarding the success or
failure of logicism?
*** Linguistics. Is there a linguistic or psycholinguistic « natural kind » corresponding to logical words?
*** History of Logic. How did
the question emerge? What are the relationships between historical
forerunners of the distinction (such as the distinction between
categoremata and syncategoremata) and the contemporary idea of logical
The workshop is organized as part of ESSLLI, August 1-12, 2011 (http://esslli2011.ijs.si). Participants are required to register at ESSLLI 2011, and can attend any other ESSLLI courses and workshops of their choice.
*** European Science Foundation (ESF)
*** The Swedish Research Council
*** ESSLLI 2011
J. van Benthem (Amsterdam and Stanford University)
Logical Constants in a Dynamical Perspective
Handout + relevant paper "Logical Constants, the various fortunes of an elusive notion" (in W. Sieg, R. Sommer, and C. Talcott eds, Reflections on the Foundations of Mathematics, Essays in Honor of Sol Feferman, ASL Lecture Notes in Logic 15, 426-446)
Abstract: In logical systems
for information flow and many-agent interaction, logical constants play
two different roles. They structure propositions, but they also
structure actions of various sorts. We will discuss this broader
theatre in general terms, trying to extend existing approaches to what
makes logical constants so special.
D. Bonnay (Paris Ouest University) and Dag Westerståhl (University of Stockholm)
Constants and Consequences
Abstract: Given an
interpreted language and a set of logical constants, Tarski's semantic
definition of logical consequence yields a consequence relation. But
given a consequence relation, is there a natural way to extract from it
a set of logical constants? In this talk, we will compare two ways of
doing so, one purely syntactical, which is based on the idea that an
expression is logical if it is essential to the validity of at least
one inference, and one semantical, which is based on the idea that
an expression is logical if its interpretation is fully determined by
the rules for its use.
K. Došen (Mathematical Institute, Serbian
Academy of Sciences and Arts, Belgrade, and Faculty of Philosophy,
University of Belgrade)
Logical Constants and Adjunction
Slides + bibliography
Abstract: The idea that
logical constants are those that can be characterized by
proof-theoretical means is related to Lawvere's thesis that logical
constants are tied to functors in adjoint situations. From the
perspective of categorial proof theory, Lawvere's thesis accords rather
well with intuitionistic logic ("rather well" and not "perfectly"
because of distribution of conjunction over disjunction). Its status
with other logics is questionable. In particular, it does not fare very
well in classical logic, although that logic can be understood sensibly
in categorial proof theory.
C. Dutilh Novaes (University of Groningen)
Syncategoremata are not logical constants
Slides + relevant paper "Reassessing logical hylomorphism..."
Abstract: The medieval concept
of syncategorematic terms is often viewed as a forerunner of the modern
concept of logical constants. However, there are significant
differences between how medieval authors conceived the role of
syncategoremata within logical theorizing and modern conceptions of
logical constants. Reflecting on the differences between the two
frameworks allows us to evaluate critically some of the assumptions and
theoretical commitments underlying current discussions on logical
constants, and this will be the goal of the present contribution.
F. Engström (University of Gothenburg)
Abstract: Dependence logic,
proposed by Väänänen, is the logic of first-order logic
plus atomic formulas for functional dependencies between variables. It
is similar to Hintikka’s Independence Friendly logic even though
there is no compositional translation between them. Still, dependence
logic and IF-logic both have the strength of existential second-order
logic on the level of sentences.
To define a compositional semantics for dependence logic we need to
consider sets of assignments called teams. There are several types of
dependencies that could be investigated in this setting: functional,
multivalued, and embedded multivalued dependence.
Dependence logic uses functional dependence as its notion of
dependence. The truth condition for the dependence atom is more or less
the same as above. However care is needed when stating the truth
conditions for complex formulas as we are dealing with sets of
assignments.Recently arguments for logics with (embedded) multivalued
dependence as its notion of dependence has been proposed. One of the
arguments is that multivalued dependence handles generalized
quantifiers better than functional dependence. We will give some
background on dependence in logic and arguments for and against the
different dependence atoms, hopefully shedding some light on the
differences between these variants of IF-logic.
S. Feferman (Stanford University)
Which quantifiers are logical? A combined semantical and inferential criterion
Slides + relevant paper "Which quantifiers are logical? A combined semantical and inferential criterion"
Abstract: The aim of logic is
to characterize the forms of reasoning that lead invariably from true
sentences to true sentences, independently of the subject matter; thus
its concerns combine semantical and inferential notions in an essential
way. Up to now most proposed characterizations of logicality of
sentence generating operations have been given either in semantical or
inferential terms. This paper offers a combined semantical and
inferential criterion for logicality (improving one originally proposed
by Jeffery Zucker) and shows that the quantifiers that are logical
according to that criterion are exactly those definable in first order
P. Galliani (University of Amsterdam)
Some denotationally indistinguishable operators
Abstract: When reasoning about
the definitions of the operators for a formal system, it can be
necessary to distinguish between the denotations of their semantic
definitions - that is, the truth conditions that they induce when
applied to suitable expressions of the language - and their
connotations, that is, the formal descriptions of the procedures to be
used in order to compute these conditions.
In this talk, I will argue that logicality cannot be
defined in terms of denotation only, and, in particular, that operators
which induce the same satisfiability condition may behave differently
with respect to the property of logicality.
In order to do so, I will discuss two equivalent semantics for
disjunction and for existential quantification in Dependence Logic, and
I will show that only one of these two semantics respects locality with
respect to extensions of Dependence Logic.
A. Giordani (Catholic University of the Sacred Heart)
Three Ways to Logicality
Abstract: Tarski characterizes logical constants in terms of
invariance under the group of all permutations on a fixed universal
domain. It is known that this account of logicality is subjected to the
objection that operators that intuitively are not considered logical,
such as numerical quantifiers, turn out to be logical on the base of
it. In the present talk three independent ways for identifying logical
operators are sketched and are shown to be consistent with
Tarski’s account in as much as second order quantifiers are
acknowledged as logical operators.
R. Kahle (New University of Lisbon), joint work with J. Alama
Logical Constants: Classical, Intuitionistic, Dialogical ?
constants are a controversial issue in the philosophy of logic. The
discussion focuses largely on generalized quantifiers and modal
operators (to name two examples) and investigates possible criteria of
demarcation. We will confine ourselves in this work to
propositional logical constants, a seemingly innocent area: the
standard sentential connectives, as "and", "or", "if . . . then" count
as logical constants, and \nothing else". But one can challenge the
distinction of these constants, when one considers the differences in
classical, intuitionistic, and dialogical logic.
M. Petrolo (University Paris VII) & A. Naibo (University Paris I) & T. Seiller (University Aix-Marseille 2)
A computational analysis of logical constants
Abstract: We investigate the
conditions used to establish what counts as a logical constant from a
proof-theoretical point of view. First, we present some limitations of
Prawitz's inversion principle. Our criticism naturally leads to an
additional requirement (eta-expansion) based on the Curry-Howard
correspondence, showing that the properties enjoyed by logical
constants have a computational nature. Nevertheless, lambda-calculus
does not allow a satisfactory reconstruction of logical inferentialism
on omputational basis rather than linguistic ones. What is needed
is a combinatorial and untyped setting in which logical types emerge
through a notion of interaction, allowing the definition of logical
constants by means of constructions on untyped objects.
T. Piecha (University of Tübingen) & W. de Campos Sanz (Federal University of Goias)
On the constructive meaning of implication in classical and intuitionistic logic
Abstract: We scrutinize two
approaches to constructive semantics put forward by Prawitz and, more
recently, by Sandqvist. Both semantics depend on extensions by
systems of production rules only. We argue that the restriction to
production rules leads to a conflation of admissibility with
derivability, generating a justification of Peirce's law and thus of
classical logic. Such a justification is avoided if basic rules
discharging basic assumptions are allowed. However, also in this wider
setting the Mints rule would be justified, implying incompleteness of
natural deduction for minimal and intuitionistic logic with respect to
the proposed semantics. Allowing for non-basic extensions prevents this
justification, but jeopardizes central aims of constructive semantics.
G. Restall (University of Melbourne)
Logical Constants, Sequent Structures and Speech Acts
Abstract: In this talk I will
consider the connections between the logicality of elements of the
vocabulary of an object language, the structural features available in
a proof system for a logic, and the different ways those structures can
be connected to kinds of speech acts (such as assertion and denial),
structural features of speech acts (including substitution and other
transformations) and transitions between speech acts (such as the
making of different kinds of suppositions).
The focus of my attention will be the hypersequent calculus for the
two-dimensional modal logic of Humberstone and Davies , and I will
consider the different ways that kinds of modal operators could be
taken to be either logical or non-logical parts of our vocabulary,
depending on what features of our structures of our discourse we
 Greg Restall “A Cut-Free Sequent System for Two Dimensional
Modal Logic, and why it matters,” Annals of Pure and Applied
Logic, to appear.
G. Sher (UC San Diego)
Logical Constants, Mathematical Constants, and Truth
Friday 12. 11.00-12.00
Abstract: In this talk I will consider the following questions:
1. What is the relation between logical and mathematical constants?
2. Are logical and mathematical constants denoting constants?
3. If they are, are their denotations “real” or fictional?
4. If their denotations are fictional, are logical and mathematical laws false?
M. Weiss (University of British Columbia)
The early Wittgenstein's critique of Frege and Russell
Abstract: After outlining
Frege's and Russell's conceptions of the subject of logic, I
reconstruct the basis of the early Wittgenstein's response that logical
constants are not representational.