arXiv subjects

Ugo de'Liguoro

Publications and source records attributed to Ugo de'Liguoro.

23 records · Page 2Linked to original sources

arXiv2014

Knowledge Spaces and the Completeness of Learning Strategies

We propose a theory of learning aimed to formalize some ideas underlying Coquand's game semantics and Krivine's realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite positive and negative information that guides a learning strategy. We use a leading example to illustrate how non-constructive proofs lead to continuous and effective learning strategies over knowledge spaces, and prove that our learning semantics is sound and complete w.r.t. classical truth, as it is the case for Coquand's and Krivine's approaches.

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arXiv2013

Proceedings First Workshop on Control Operators and their Semantics

The focus of the papers presented in this volume is on the interplay between syntax and semantics in case of languages, namely the central question of what a program means and how it does define the intended procedure. This is a crucial issue especially in the case of control operators, since they are as powerful as potentially obscure, and programs that use them are usually more error-prone than purely declarative ones. The included contributions provide perspectives on the topic of control operators via operational semantics of formal calculi as well as type assignment systems, denotational semantics, game semantics, category theory and logic.

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arXiv2013

Characterisation of Strongly Normalising lambda-mu-Terms

We provide a characterisation of strongly normalising terms of the lambda-mu-calculus by means of a type system that uses intersection and product types. The presence of the latter and a restricted use of the type omega enable us to represent the particular notion of continuation used in the literature for the definition of semantics for the lambda-mu-calculus. This makes it possible to lift the well-known characterisation property for strongly-normalising lambda-terms - that uses intersection types - to the lambda-mu-calculus. From this result an alternative proof of strong normalisation for terms typeable in Parigot's propositional logical system follows, by means of an interpretation of that system into ours.

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arXiv2012

Proceedings Fourth Workshop on Classical Logic and Computation

CL&C'12 was the fourth of a conference series on "Classical Logic and Computation", held as satellite to ICALP'12 on Sunday July 8, 2012 in Warwick, England. CL&C intends to cover all work aiming to explore computational aspects of classical logic and mathematics, and is focused on the exploration of the computational content of mathematical and logical principles. The scientific aim of this workshop is to bring together researchers from both fields and exchange ideas. The intention of the organisers is for CL&C to be an informal workshop. Participants are encouraged to present work in progress, overviews of more extensive work, and programmatic/position papers, as well as completed projects. Submission of both short abstracts and of longer papers were invited. Four submissions were accepted as full papers and are included in these proceedings. Three more were accepted only as communications for the conference. Paulo Oliva gave an invited talk on "Some connections between Game Theory and Proof Theory".

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arXiv2010

Interactive Realizers and Monads

We propose a realizability interpretation of a system for quantifier free arithmetic which is equivalent to the fragment of classical arithmetic without "nested" quantifiers, called here EM1-arithmetic. We interpret classical proofs as interactive learning strategies, namely as processes going through several stages of knowledge and learning by interacting with the "environment" and with each other. We give a categorical presentation of the interpretation through the construction of two suitable monads.

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