Electronic Notes in Theoretical Computer Science (ENTCS)

Alves presented in his PhD thesis a normalization procedure for N-Graphs, a multiple conclusion natural deduction for propositional classical logic proposed by de Oliveira in 2001, with proofs as directed graphs. Here we develop a new normalization for ...

Logic-based approaches for analyzing and evaluating arguments have been largely studied in recent years, yielding a variety of formal methods for argumentation-based reasoning. The goal of this paper is to provide an abstract, proof theoretical ...

Nominal rewriting generalises first-order rewriting by providing support for the specification of binding operators. In this paper, we give sufficient conditions for (local) confluence of closed nominal rewriting theories, based on the analysis of rule ...

Nominal systems are an alternative approach for the treatment of variables in computational systems. In the nominal approach variable bindings are represented using techniques that are close to first-order logical techniques, instead of using a higher-...

We characterize β-strongly normalizing λ-terms by means of a non-idempotent intersection type system. More precisely, we first define a memory calculus K together with a non-idempotent intersection type system K, and we show that a K-term t is typable ...

The kinds of inference rules and decision procedures that one writes for proofs involving equality and rewriting are rather different from proofs that one might write in first-order logic using, say, sequent calculus or natural deduction. For example, ...

We formulate principles of induction and recursion for a variant of lambda calculus in its original syntax (i.e., with only one sort of names) where α-conversion is based upon name swapping as in nominal abstract syntax. The principles allow to work ...

We introduce Canonical HybridLF (CHLF), a metalogic for proving properties of deductive systems, implemented in Isabelle HOL. CHLF is closely related to two other metalogics. The first is the Edinburgh Logical Framework (LF) by Harper, Honsell and ...

This paper describes a fibrational categorical semantics for the modal necessity-only fragment of constructive modal type theory, both with and without dependent types. Constructive type theory does not usually discuss logical modalities, and modalities ...

In this work, we will reason on how a given focused proof, where atoms are assigned with some polarity, can be transformed into another focused proof, where the polarity assignment to atoms is changed. This will allow, in principle, transforming a proof ...

Traditional proof theory of Propositional Logic deals with proofs whose size can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The use of proof-graphs, instead of ...

In this paper we prove the correctness of a compiler for a call-by-name language using step-indexed logical relations and biorthogonality. The source language is an extension of the simply typed lambda-calculus with recursion, and the target language is ...

We present a graph approach to intuitionistic modal logics, which provides uniform formalisms for expressing, analysing and comparing Kripke-like semantics. This approach uses the flexibility of graph calculi to express directly and intuitively possible-...

Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form xy which decompose a compound data structure into its parts. Typing ...