Saturday, May 21 9:45 - 10:30
I will present some puzzles about conditional knowledge ascription — about things of the form 'A knows that if p, then q.' The puzzles suggest, I’ll argue, that some true knowledge ascriptions do not relate knowers to truths, that the factivity of 'knows' isn’t easily written into its semantics, and that indicative conditionals don't express propositions.
Saturday, May 21 10:30 - 11:15
Necessity Under "Only"
A well-known compositionality problem involves the interaction between "only" and goal-oriented modality: "only" can weaken a necessity statement and a necessity modal can suspend a characteristic inference associated with "only." Existing proposals all resort to non-standard assumptions either about "only" or what it combines with. This talk will show that a standard analysis of "only" and a plausible analysis of goal-oriented modality can make sense of the special properties of the interaction between "only" and goal-oriented necessity and can account for the compositionality problem.
Saturday, May 21 11:15 - 12:00
Implicatives: What Has Been Done and What Needs to Be Done
From the late sixties on, implicative predicates, exemplified in ‘Joan managed to finish her paper’, were one of the topics Lauri Karttunen returned to in his research but even at the end of his life he felt they hadn’t gotten enough attention. I will try summarize some of the work done by him and his collaborators or inspired by him on both the at issue and not at issue components of the meaning of implicative expressions.
Burkhard Schipper & Gaia Belardinelli
Saturday, May 21 14:45 - 15:30
On Notions of Knowledge Beneath Levels of Awareness
There are various different notions of implicit knowledge in logic, computer science, psychology, psychoanalysis, sociology etc. A common feature is that they refer to knowledge beneath some level of awareness. We then study some of these notions in unawareness structures, which are extensions of Kripke structures that feature a complete lattice of state-spaces allowing for asymmetric awareness (in addition to explicit knowledge). Their event-based semantics lends itself easily to applications in game theory and decision theory. Yet, so far they lack any notion of implicit knowledge. In this talk, we first show to what extent implicit knowledge à la Fagin and Halpern (1988) is derivable from explicit knowledge and vice versa. Second, we extend unawareness structures to tacit knowledge à la Polanyi (1962, 1966). This enables us to study tacit knowledge in decision theory, game theory, mechanism design, and other applications. We then discuss to what extent we can empirically identify an agent's tacit knowledge from her actions. Third, we give up some idealized properties of implicit knowledge such as reflexivity and introspection in order to capture descriptive notions of implicit knowledge in psychology. This allows us to model implicit biases, amnesic syndrome, blindsight, and failures of implicit contingent reasoning.
Saturday, May 21 15:30 - 16:15
Possibilities for Awareness
Possibility Semantics is a generalization of Possible World Semantics, based on partial possibilities instead of complete possible worlds. In recent years, this approach has been applied to the semantics of modal and nonclassical logics, natural language semantics, and semi-constructive mathematics. In this talk, I will discuss how notions of "unawareness" studied in economics and computer science can be represented in the framework of Possibility Semantics.
Johan van Benthem
Saturday, May 21 16:15 - 17:00
Topological Dependence, A Case Study in Epistemic Mathematics (joint work with Alexandru Baltag)
While epistemic logic is a theory of information as semantic range,dependence reflects a further broad intuition of information as correlation. We explore how dependence functions in a topological setting for empirical inquiry where open sets are outcomes of possible measurements and epistemically useful dependencies are continuous maps. Having determined the base logic, we go on to discuss the epistemic import of independence, uniform continuity, and topological computability on Scott domains.
Sunday, May 22 9:30 - 10:15
Causal Models at Multiple Levels of Granularity
In many scientific domains, a causal description of the system under investigation is considered the ultimate goal of research, because a causal description enables predictions of how the system will behave under intervention. But since a system can be described at multiple levels of granularity, the question arises of how to select the right level of granularity, whether there is such a privileged level or whether any level permits a causal description. This talk will provide a brief overview of some of the different approaches that have been taken to address this question, and what the underlying principles are that guide these approaches.
Sunday, May 22 10:15 - 11:00
Distributional Robustness, Replicability, and Causality
How can we draw trustworthy scientific conclusions? One criterion is that a study can be replicated by independent teams. While replication is critically important, it is arguably insufficient. If a study is biased for some reason and other studies recapitulate the approach then findings might be consistently incorrect. It has been argued that trustworthy scientific conclusions require disparate sources of evidence. However, different methods might have shared biases, making it difficult to judge the trustworthiness of a result. We formalize this issue by introducing a "distributional uncertainty model", which captures biases in the data collection process. Distributional uncertainty is related to other concepts in statistics, such as confounding and selection bias. We show that a stability analysis on a single data set allows to construct confidence intervals that account for both sampling uncertainty and distributional uncertainty. The proposed method is inspired by a stability analysis that is advocated for by many researchers in causal inference.
Sunday, May 22 11:00 - 11:45
Causal Models in Philosophy
Philosophers have used a variety of formalisms to represent and analyze concepts of interest, especially mathematical logic and probability theory. More recently, they have made use of causal models, including graphical causal models and structural equation models. The most immediate application of these tools is to explicate the epistemology of causal relations. In my talk, I will illustrate applications of causal models in other areas philosophy: the interpretation of probability, and decision theory.
Valeria de Paiva
Sunday, May 22 14:30 - 15:15
Dialectica Categories Revisited
Gödel's Dialectica interpretation was conceived as a tool to obtain the consistency of Peano arithmetic via a proof of consistency of Heyting arithmetic, in the 40s. In recent years, several proof-theoretic transformations, based on Gödel's Dialectica interpretation, have been used systematically (by Kohlenbach and others) to extract new content from classical proofs, following a suggestion of Kreisel. Thus, the interpretation has found new relevant applications in several areas of mathematics and computer science. Several authors have explained the Dialectica interpretation in categorical terms. In particular, I have introduced the notion of a Dialectica category as an internal version of Gödel's Dialectica Interpretation in my doctoral thesis, written under Hyland's supervision. This categorical Dialectica construction has been generalized in many meaningful directions, and it has had many applications developed from it, from concurrency theory and Petri nets, from linear logic models of state and games, to Set Theory and `small cardinals'. Recently the construction has been under scrutiny, as many applications in computing, especially ones using lenses and bidirectional transformations have been discussed, as well as other applications using Spivak's category of polynomials. This is all part of a growing movement on Applied Category Theory, of which the Topos Institute is one of the centers and that we will also discuss.
Sunday, May 22 15:15 - 16:00
On the Expressive Power of Homomorphism Counts
A classical result by Lovász asserts that two graphs G and H are isomorphic if and only if they have the same left profile, that is, for every graph F, the number of homomorphisms from F to G coincides with the number of homomorphisms from F to H. A similar result is also known to hold for right profiles, that is, the number of homomorphisms from G to F and from H to F. In recent years, there has been a study of equivalence relations obtained by restricting the left profile or the right profile to a particular class of graphs, instead of the class of all graphs. For example, Dvorák has shown that equivalence in counting logic with a fixed number of variables can be captured by left profiles restricted to the class of graphs of bounded treewidth. The aim of this talk is to present an overview of these results and to discuss the differences in expressive power between left homomorphism counts and right homomorphism counts.
Sunday, May 22 16:00 - 16:45
Non-Classical Metatheory from Above
This will be a talk on the extent to which non-classical logicians can prove results about their favored non-classical logic L using only the logical resources of L in the metalanguage. In particular I will look at the extent to which non-classical logicians can prove results about L using L in the metalanguage, but classical logic in the metametalanguage. One might have hoped that we could use such results to tell us something useful about the prospects of proving results about L internal to L. In this talk I show that this hope appears to be in vain — showing how, with particular focus on the case of intuitionistic propositional logic, results proved with a classical metametalanguage do not accurately reflect the behavior of a truly internalized metatheory.
Saturday, May 21 13:30 - 14:00
Two Modal Principles in Aristotle’s Metaphysics Θ.4
I will consider two modal principles that show up in Aristotle’s Metaphysics Theta. These principles have been at the centre of much controversy in recent scholarship. Indeed, one of them seems blatantly false. I’ll discuss some recent attempts to formalise them in propositional modal logic, and note the sorts of problems these attempts run into. Towards the end, I’ll mention an alternative interpretation of these principles in terms of Aristotle’s own modal syllogistic. This approach, I think, may be more promising in helping us see exactly why Aristotle accepts the two principles and what they amount to.
Saturday, May 21 14:00 - 14:30
I identify a type of introspection, dynamic introspection, which, I argue, has been mostly ignored in epistemology. Dynamic introspection concerns how we come to know, rather than just what we know. My aim is to briefly show how the tools of dynamic epistemic logic can be used to reason about epistemic agents with and without dynamic introspection, and to demonstrate the relevance of such reasoning to epistemology.
Sunday, May 22 12:00 - 12:30
Causal Abstraction and Computational Explanations in Artificial Intelligence
Theories of causal abstraction are a bridge between symbolic and connectionist models of computations, allowing for formally precise accounts of when a symbolic computation is implemented by a neural network. I will present on recent work where we both (1) analyze neural networks to determine whether they implement a hypothesized symbolic computation and (2) train neural networks to implement a target symbolic computation.
Sunday, May 22 12:30 - 13:00
Algorithms and Determinism
Traditionally, algorithms have been analysed in terms of one of the standard models of computation, incorporating features of effective procedures like finiteness, unambiguity and determinism. However, it is unclear how these features should be applied in modern discussions of named algorithms. In this talk I will focus on the nature of determinism in algorithms. Through a 'deterministic' algorithm case study, I will argue that determinism in algorithms should be traced to correctness and implementation conditions, rather than being a feature of algorithms themselves (as we would expect from standard models of computation).