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Reflections on Symmetry
 Complementizers and WH Constructions
, 2002
"... Abstract. Whilst it is generally accepted as a positive criterion, affordance only gives the weakest of hints for interactive systems designers. This paper shows how useful it is to consider affordance as generated by a correspondence between program symmetries and user interface symmetries. Symmetr ..."
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Cited by 7 (4 self)
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Abstract. Whilst it is generally accepted as a positive criterion, affordance only gives the weakest of hints for interactive systems designers. This paper shows how useful it is to consider affordance as generated by a correspondence between program symmetries and user interface symmetries. Symmetries in state spaces (for instance, as might be visualised in statecharts) can be carried through to user interfaces and into user manuals, with beneficial results. Exploiting affordances, understood in this way, in addition to their well known user interface benefits, makes programs simpler and more reliable, and makes user manuals shorter. 1
The Cost of a Cycle is a Square
, 1999
"... The logical flow graphs of sequent calculus proofs might contain oriented cycles. For the predicate calculus the elimination of cycles might be nonelementary and this was shown in [Car96]. For the propositional calculus, we prove that if a proof of k lines contains n cycles then there exists an ..."
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Cited by 3 (2 self)
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The logical flow graphs of sequent calculus proofs might contain oriented cycles. For the predicate calculus the elimination of cycles might be nonelementary and this was shown in [Car96]. For the propositional calculus, we prove that if a proof of k lines contains n cycles then there exists an acyclic proof with O(k n+1 ) lines. In particular, there is a quadratic time algorithm which eliminates a single cycle from a proof. These results are motivated by the search for general methods on proving lower bounds on proof size and by the design of more efficient heuristic algorithms for proof search.
Streams and Strings in Formal Proofs
"... Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. ..."
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Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. In our approach, "logic" is often forgotten and combinatorial properties of graphs are taken into account to explain logical phenomena.
Complexity and ordinary life, and some mathematics in both
, 2003
"... What is mathematics, exactly? This is a somewhat complicated question, with no simple answer. In any event, mathematics is like a large place, with many regions and villages, and many different ways of doing things. One can also try to make up new ways of doing things, in connection with whatever mi ..."
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What is mathematics, exactly? This is a somewhat complicated question, with no simple answer. In any event, mathematics is like a large place, with many regions and villages, and many different ways of doing things. One can also try to make up new ways of doing things, in connection with whatever might be of interest. Let us look here at a few points which can come up naturally in ordinary life, as well as involve some substantial mathematics (in some of their forms). Differences between answers of “yes ” and “no” Imagine the following kind of question: “Does soandso have a pencil in his or her office?” If someone finds a pencil in the office, then that provides a way in which an answer of “yes ” can be clearly established. The pencil can simply be shown. An answer of “no ” is quite different, and apparently more complicated. How can one establish an answer of “no”, without just going through all of the contents of the office?