We define a type inference system for Nominal Rewriting where the types associated to terms are polymorphic (built from a set of base data sorts, type variables, and user-defined type constructors). In contrast with standard term rewriting systems or the λ-calculus, a typing environment for nominal rewriting includes type information for atoms, variables and function symbols. We give a syntax-d...

We develop the coalgebraic theory of nominal Kleene algebra, including an alternative language-theoretic semantics, a nominal extension of the Brzozowski derivative, and a bisimulation-based decision procedure for the equational theory.

Recently, a very general description logic (DL) that extends SROIQ (the DL underlying OWL 2 DL) at the same time with nominal schemas and epistemic modal operators has been proposed, which encompasses some of the most prominent monotonic and non-monotonic rule languages, including Datalog under the answer set semantics. A decidable fragment is also presented, but the restricted language does no...

Nominal schemas have recently been introduced as a new approach for the integration of DL-safe rules into the Description Logic framework. The efficient processing of knowledge bases with nominal schemas remains, however, challenging. We address this by extending the well-known optimisation of absorption as well as the standard tableau calculus to directly handle the (absorbed) nominal schema a...

When reasoning about inductively defined predicates, such as typing judgements or reduction relations, proofs are often done by a case analysis on the last rule of a derivation. In HOL and other formal frameworks this case analysis involves solving equational constraints on the arguments of the inductively defined predicates. This is well-understood when the arguments consist of variables and i...

Quantification and nominal anaphora is a rich and complex area of research, which has attracked many people; especially since the development of dynamic semantics in the early eigthies. One way to obtain a systematic view on this field, is to focus on the quantificational resources employed to interpret anaphoric relationships. In this article, I will develop such a view as far as first-order q...

The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computationorie...

This thesis studies two major extensions of nominal terms. In particular, we study an extension with λ-abstraction over nominal unknowns and atoms, and an extension with an arguably better theory of freshness and α-equivalence. Nominal terms possess two levels of variable: atoms a represent variable symbols, and unknowns X are ‘real’ variables. As a syntax, they are designed to facilitate metap...

FIROUGHOUT 1989, popular wisdom held that the U.S. monetary authority was faced with a daunting policy task: it should not permit too much money growth and cause prices to rise too rapidly, but it should not allow too little money growth and cause the economy to tip into recession as real output would fall. Sympathy for monetary policymakers, however, is not necessarily widespread among economi...