We search for alternative musical scales that share the main advantages of classical scales: pitch frequencies that bear simple ratios to each other, and multiple keys based on an underlying chromatic scale with tempered tuning. We conduct the search by formulating a constraint satisfaction problem that is well suited for solution by constraint programming. We find that certain 11-note scales o...

The paper presents a simple format for typed logics with states by adding a function for register update to standard typed lambda calculus. It is shown that universal validity of equality for this extended language is decidable (extending a well-known result of Friedman for typed lambda calculus). This system is next extended to a full fledged typed dynamic logic, and it is illustrated how the ...

Reliability-based design optimization is concerned with designing a product to optimize an objective function given uncertainties about whether various design constraints will be satisfied. However, the widespread practice of formulating such problems as chance-constrained programs can lead to misleading solutions. While a decision analytic approach would avoid this undesirable result, many eng...

Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calc...

The early phases of syntactic acquisition are characterized by many input frequency and item effects, which argue against theories assuming innate access to classical syntactic categories. In formulating an alternative view, we consider both prototype and exemplar-learning models of categorization. We argue for a ‘hybrid’ usage-based view in which acquisition depends on exemplar learning and re...