These tutorial notes present nominal game semantics, a denotational technique for modelling higher-order programs. A. S. Murawski and N. Tzevelekos. Nominal Game Semantics. Foundations and TrendsR © in Programming Languages, vol. 2, no. 4, pp. 191–269, 2015. DOI: 10.1561/2500000017.

Nominal unification calculates substitutions that make terms involving binders equal modulo alphaequivalence. Although nominal unification can be seen as equivalent to Miller’s higher-order pattern unification, it has properties, such as the use of first-order terms with names (as opposed to alphaequivalence classes) and that no new names need to be generated during unification, which set it cl...

Equation solving between nominal terms has been investigated by several authors, who designed and analyzed algorithms for nominal unification [3, 4, 15, 26], nominal matching [5], equivariant unification [6], permissive nominal unification [8]. However, in contrast to unification, its dual problem, anti-unification, has not been studied for nominal terms previously. In [18], it is referred to a...

In this extended abstract, we review our recent work “Nominal Schemas in Description Logics: Complexities Clarified” [6], to be presented at KR 2014. The fruitful integration of reasoning on both schema and instance level poses a continued challenge to knowledge representation and reasoning. While description logics (DLs) excel at the former task, rule-based formalisms are often more adequate f...