This is work with Baudisch and Martin-Pizarro which applies the Hrushovski-Fraisse amalgamation procedure to obtain a theory of fields, of prime characteristic of Morley rank 2, equipped with a definable additive subgroup of rank 1.
We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms, according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; threshold-sensitive conditions such as "preface" rules.
(In the late 80's) J. Paris asked whether or not \Delta_n induction implies \Sigma_n collection. In this talk wesketch alternative proofs of(recent) results of T. Slaman and N. Thapen concerning this problem for the casen=1. Our proofs use (old) results (of C. Dimitracopoulos and J. Paris) concerning relationships between \Sigma_n collection and \Sigma_n pigeonhole principle.
Traditionally, fuzzy logic is introduced by imposing certain restrictions on the truth-functions of propositional connectives in [0,1], which lead to the notion of continuous t-norm. I shall present a completely different view independent of the original [0,1] semantics, which regards fuzzy logic rather as a system of inference rules that preserve partial truth. This approach provides a natural justification for the whole family of fuzzy logics presently studied by the theoretical fuzzy community, and shows the position of fuzzy logics in the logical landscape (esp. their relation to substructural logics).
We define and examine a notion of logical friendliness, which is a natural broadening of the familiar notion of classical consequence, obtained by playing with the quantifiers in the standard definition of classical consequence. It is formulated first in its simplest form, and then in a syntax-independent version, which we call sympathy. Although born of idle curiosity, the concept makes contact with a surprising range of notions and operations familiar in the history of logic from 1847 to the present.
A guided tour through the highlights of Brouwer's intuitionism(!)
We develop a welfarist egalitarian argument for degressively proportional weights in a federal assembly. The argument is based on the idea that countries in a federation are like larger or smaller cartels of social units and that the formation of cartels of unequal size upsets the equality between the expected utilities that countries receive from proposals. Drawing on a probabilistic model, we show which particular degressively proportional weighting should be chosen. We also discuss the relation between our argument and the voting-power argument in favour of degressive proportionality.
Despite the hopes expressed by Kemeny in 1954 that Inductive
Logic in the sense of W.E.Johnson and Rudolf Carnap would next be
pushed from the purely unary predicate languages considered up to
that time to higher arities nothing along these lines was attempted
over the following half century. This despite the fact that in the real
world we do on occasions apply inductive reasoning to at least binary
In this talk I shall describe an attempt by Chris Nix and myself to generalize the Johnson-Carnap methodology to binary languages which results in some slightly unexpected conclusions.