Typing rules and structural operational semantics are often given via inference rules: that is, the justification of a typing or an evaluation is actually a proof. Thus it is not surprising that proof theory can be used to benefit the specification of and the reasoning about computation. An additional advantage of using proof theory is that it can support such “intensional” aspects of computati...

We refine a model for linear logic based on two well-known ingredients: games and simulations. We have already shown that usual simulation relations form a sound notion of morphism between games; and that we can interpret all linear logic in this way. One particularly interesting point is that we interpret multiplicative connectives by synchronous operations on games. We refine this work by giv...

The logic of ACL2 is descended from λ-calculus via Common LISP. It is well-known that this logic is su cient to reason about arbitrary computations. However, λ-calculus is not today's dominant programming paradigm. To reason about today's programs, as opposed to today's computations, we need a logic that supports modern programming practices. In this paper, we present an approach that allows AC...

Prerequisites • Good skills in functional programming (e.g., from the FMFP course) • Knowledge about logic and the λ-calculus (e.g., from the FMFP course)

Gödel’s modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models. The first is the modal logic GL, also known as the Provability Logic, which was shown in 1979 by Solovay to be the logic of the formal provability predicate. The second is Gödel’s original modal logic of provability S4, together with its explicit coun...

Given a normal (multi-)modal logic Θ, a characterization is given of the finitely presentable algebras A whose logics LA split the lattice of normal extensions of Θ. This is a substantial generalization of [Rautenberg, 1980; Rautenberg, 1977] in which Θ is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by [Blok, 1978] that for all cycle-free ...

An adaptive minimummean-square error (MMSE) array receiver based on the fuzzy-logic recursive least-squares (RLS) algorithm is developed for asynchronous DS-CDMA interference suppression in the presence of frequency-selective multipath fading. This receiver employs a fuzzy-logic control mechanism to perform the nonlinear mapping of the squared error and squared error variation, denoted by (e2,Δ...

The Kronecker product of two Schur functions s λ and s µ , denoted s λ * s µ , is defined as the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group indexed by partitions of n, λ and µ, respectively. The coefficient, g λ,µ,ν , of s ν in s λ * s µ is equal to the multiplicity of the irreducible representation indexed by ν in the tensor product...

These lectures summarize and organize the material appearing in: Smoke and Mirrors: Combinatorial properties of small cardinals equiconsistent with huge cardinals. • Much of the early history of logic in general and model theory in particular was tied up with understanding the expressive power of first and second order logic (and their variants). • One distinguishing feature of first order logi...

Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the λ-binder of the lambda-calculus or the ∀binder of first-order logic. It also allows us to finitely axiomatise arithmetic, and similarly to axiomatise ‘nominal’ datatypes-with-binding. Just like ...