## Past Events › Applied Logic Seminar

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## Dynamic Definitions

Speaker Jeremy Seligman Abstract A definition formulated correctly using necessary and sufficient conditions introduces new vocabulary via an interpretation in a familiar language. A recursive definition introduces the application of vocabulary to new objects in terms of previously understood applications to other, typically less complex, objects. A circular definition, such as the definition of truth that plagues our attempts to understand self-referential truth claims, may change the predicate that it defines. In this talk, I will reflect on a conception…

Find out more »## Epistemic logic for sceptical agents

Speaker Marta Bílková Title Epistemic logic for sceptical agents Abstract We present an epistemic logic for a notion of knowledge confirmed by a reliable source of information. Such notion of knowledge can be modelled as a diamond modality over a substructural logic. As the weakest propositional background logic we choose distributive non-associative full Lambek calculus with a negation and work with its relational semantics, interpreting the elements of a relational frame as information states consisting of collections of data which…

Find out more »## Filtrations in Intermediate Logics via Locally Finite Reducts of Heyting Algebras

Speaker Nick Bezhanishvili Abstract There are two standard model-theoretic methods for proving the finite model property for modal and intermediate logics, the standard filtration and selective filtration. The standard filtration for modal and intuitionistic logics was first defined algebraically by McKinsey and Tarski in the 1940’s. In the 1960’s Lemon and Segerberg defined filtrations model theoretically. Selective filtrations were introduced by Gabbay and further developed by Fine and Zakharyaschev (1970’s and 1980’s). In this talk I will give an algebraic…

Find out more »## Categorical Decision Theory

Speaker Marcus Pivato (Université de Cergy-Pontoise, France) Abstract (Joint work with Vassili Vergopoulos of the Paris School of Economics) Individuals and societies must often make difficult decisions, which are fraught with uncertainty. How should an agent decide when faced with such uncertainty? This is the subject of a branch of theoretical economics called Decision Theory. Bernoulli (1738) claimed that we should choose the alternative which yields the highest expected utility. But what justifies this methodology? Savage (1954) showed that, if…

Find out more »## Quantifying the Classical Impossibility Theorems from Social Choice

Speaker Frank Feys Abstract Social choice theory studies mathematically the processes involved when groups of people make choices. There are a number of beautiful and astonishing qualitative results in this area, for example Arrow’s Theorem about the non-existence of ideal voting schemes, and the Gibbard-Satterthwaite Theorem about the manipulation of elections. These classical theorems have had tremendous impact on the field of social choice. More recently, a sequence of stronger, quantitative versions of such theorems, by Gil Kalai, Ehud Friedgut,…

Find out more »## Substructural Fuzzy-relevance Logic

Speaker Eunsuk Yang Abstract This talk proposes a new topic in substructural logic joining the fields of relevance and fuzzy logics. We first introduce fuzzy systems satisfying an old relevance principle, i.e., Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm (based) systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication (without distributivity) and its neighbors. The algebraic structures corresponding to the systems are then defined, and…

Find out more »## Epistemic Updates on Algebras

Speaker Zeinab Bakhtiari Abstract The Logic of Epistemic Actions and Knowledge is an expansion of classical modal logic introduced by A. Baltag, L. S. Moss and S. Solecki as a framework for reasoning about knowledge in a dynamic logic setting. A. Kurz and A. Palmigiano recently showed that duality theory provides a flexible framework for modelling epistemic changes, which allows one to develop dynamic epistemic logics on a propositional basis that is weaker than classical logic (e.g. an intuitionistic basis).…

Find out more »## Axiomatizations of DEL-like Logics via ETL-like Method

Speaker Yanjing Wang (Department of Philosophy - Peking University) Abstract In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a "core set" of the so-called "reduction axioms". In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL without additional axioms and rules. In fact, many of the intuitive axioms and…

Find out more »## Finding A Category That Captures Modified Realizability With Extensional Equality

Speaker Yuning Feng Abstract Realizability is about interpreting logical statements with programs. A statement is realizable if we can argue for it following some programs. In this talk, we discuss a variant of realizability on typed arithmetic: it has extensional equality, and to interprete an implication, a realizing program need to be total with respect to the antecedent's type. As a formal theory, much of this realizability is known using proof-theoretic methods, and the canonical model for it is well-known.…

Find out more »## Dependence and Independence in Social Choice Theory

Speaker Eric Pacuit Abstract The modern era in social choice theory started with Ken Arrow's ground-breaking impossibility theorem. Arrow showed that there is no preference aggregation method satisfying a minimal set of desirable properties. Social choice theory has since grown into a large and multi-faceted research area. In this talk, I focus on one type of theorem studied by social choice theorists: axiomatic characterizations of preference aggregation methods. The principles studied by social choice theorists are intended to identify procedures…

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