Propagators and Solvers for the Algebra of Modular Systems

To appear in the proceedings of LPAR 21. Solving complex problems can involve non-trivial combinations of distinct knowledge bases and problem solvers. The Algebra of Modular Systems is a knowledge representation framework that provides a method for formally specifying such systems in purely semantic terms. Formally, an expression of the algebra defines a class of structures. Many expressive formalism used in practice solve the model expansion task, where a structure is given on the input and an expansion of this structure in the defined class of structures is searched (this practice overcomes the common undecidability problem for expressive logics). In this paper, we construct a solver for the model expansion task for a complex modular systems from an expression in the algebra and black-box propagators or solvers for the primitive modules. To this end, we define a general notion of propagators equipped with an explanation mechanism, an extension of the alge- bra to propagators, and a lazy conflict-driven learning algorithm. The result is a framework for seamlessly combining solving technology from different domains to produce a solver for a combined system.Comment: To appear in the proceedings of LPAR 2

Electronic Locator of Vertical Interval Successions (ELVIS): The first large data-driven research project on musical style

The ELVIS project had three locally based teams (in Canada, at McGill, in Scotland, at Aberdeen, and in New England, USA, divided between MIT, the lead, and Yale), each of which focused on a different aspect of the overall research program: using computers to understand musical style. The central unifying concept of the ELVIS project was to study counterpoint: the way combinations of voices in polyphonic music (e.g. the soprano and bass voices in a hymn, or the viola and cello in a string quartet, as well as combinations of more than two voices) interact: i.e. what are the permissible vertical intervals (notes from two voices sounding at the same time) for a particular period, genre, or style. These vertical intervals, connected by melodic motions in individual voices, constitute Vertical Interval Successions. In more modern terms, this could be described as harmonic progressions of chords, but what made ELVIS particularly flexible was its ability to bridge the gap to earlier, contrapuntally-conceived music by using the diad (a two-note combination) rather than the triad (a combination of three notes in particular arrangements) as a basis (since triads and beyond may be expressed as sums of diads)

Even shorter proofs without new variables

Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning. Interference-based methods have been proven effective, and some theoretical work has been undertaken to better explain their limits and semantics. In this work, we combine the subsumption redundancy notion from (Buss, Thapen 2019) and the overwrite logic framework from (Rebola-Pardo, Suda 2018). Natural generalizations then become apparent, enabling even shorter proofs of the pigeonhole principle (compared to those from (Heule, Kiesl, Biere 2017)) and smaller unsatisfiable core generation.Comment: 21 page