We formulate a general institution-independent (i.e. independent of the details of the actual logic formalised as institution) version of the Craig Interpolation Theorem and prove it in dependence of Birkhoff-style axiomatizability properties of the actual logic. We formalise Birkhoff-style axiomatizability within the general abstract model theoretic framework of institution theory by the novel...

Many security properties of cryptographic protocols can be all formalized as specific instances of a general scheme, called Generalized Non Deducibility on Composition (GNDC ). This scheme derives from the NDC property we proposed a few years ago for studying information flow in computer systems. The theory is formulated for CryptoSPA, a process algebra we introduced for the specification of cr...

We show how to estimate (1) the number of functions that can be implemented by a particular network architecture, (2) how much analog precision is needed in the connections in the network, and (3) the number of training examples the network must see before it can be expected to form reliable generalizations. Generality versus Training Data Required Consider the following objectives: First, the ...

Many hard problems can be solved efficiently when the input is restricted to graphs of bounded treewidth. By the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the treewidth of the input graph. Moreover, for every fixed k ≥ 0, such problems can be solved in linear time on graphs of treewidth at ...

Hyper-heuristics are easy-to-implement emerging search and optimisation strategies which have been used instead of meta-heuristics for providing higher level generalized structures to solve mainly combinatorial optimisation problems. The motivation behind them is generally expressed as raising the level of generality. That is, they are the answers to the following question: How can we create or...

We should not admit categorial restrictions on the significance of syntactically well formed strings. Syntactically well formed but semantically absurd strings, such as ‘Life’s but a walking shadow’ and ‘Caesar is a prime number’, can express thoughts; and competent thinkers both are able to grasp these and ought to be able to. Gareth Evans’ generality constraint, though Evans himself restricte...

This paper presents and compares FG and Eu, two recent formalizations of Euclid’s diagrammatic arguments in the Elements. The analysis of FG, developed by the mathematician Nathaniel Miller, and that of Eu, developed by the author, both exploit the fact that Euclid’s diagrammatic inferences depend only on the topology of the diagram. In both systems, the symbols playing the role of Euclid’s dia...

From an evolutionary point of view, what is most overwhelmingly in need of explanation is the generality of human cognition, as compared to that of our immediate ancestors. Humans sing operas, build diesel engines and agonise about domain dependence. Above all they can sustain the kinds of societies required for each of these activities. What part a domain specialist apparatus plays in this new...

Recent evidence suggests that massive amounts of practice of the basketball free throw (a "set shot") results in the development of a specific memory representation that is unique to this one shot distance and angle, and that is distinct from set shots taken at locations other than the free throw line. We termed this unique capability an especial skill. In this article, we review the evidence a...

We prove game-theoretic generalizations of some well-known zero-one laws. Our proofs make the martingales behind the laws explicit, and our results illustrate how martingale arguments can have implications going beyond measure-theoretic probability.