Valeria de Paiva

A Term Calculus for Intuitionistic Linear Logic

In this paper we consider the problem of deriving a term assignment system for Girards Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky [1]) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) and subject reduction (reduction on terms is well-typed). We also consider term reduction arising from cut-elimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these and consider their computational content.

Categorical and Kripke Semantics for Constructive S4 Modal Logic

We consider two systems of constructive modal logic which are computationally motivated. Their modalities admit several computational interpretations and are used to capture intensional features such as notions of computation, constraints, concurrency, etc. Both systems have so far been studied mainly from type-theoretic and category-theoretic perspectives, but Kripke models for similar systems were studied independently. Here we bring these threads together and prove duality results which show how to relate Kripke models to algebraic models and these in turn to the appropriate categorical models for these logics.

Making ontologies work for resolving redundancies across documents

Producing normalized representations from different ways of expressing the same idea.

Entailment, intensionality and text understanding

We argue that the detection of entailment and contradiction relations between texts is a minimal metric for the evaluation of text understanding systems. Intensionality, which is widespread in natural language, raises a number of detection issues that cannot be brushed aside. We describe a contexted clausal representation, derived from approaches in formal semantics, that permits an extended range of intensional entailments and contradictions to be tractably detected.

Full intuitionistic linear logic (extended abstract)

Abstract In this paper we give a brief treatment of a theory of proofs for a system of Full Intuitionistic Linear Logic. This system is distinct from Classical Linear Logic, but unlike the standard Intuitionistic Linear Logic of Girard and Lafont includes the multiplicative disjunction par. This connective does have an entirely natural interpretation in a variety of (non-classical) categorical models of Intuitionistic Linear Logic. The main proof-theoretic problem arises from the observation of Schellinx that cut elimination fails outright for an intuitive formulation of Full Intuitionistic Linear Logic; the nub of the problem is the interaction between par and linear implication. We present here a term assignment system which gives an interpretation of proofs as some kind of non-deterministic function. In this way we find a system which does enjoy cut elimination. The system is a direct result of an analysis of the categorical semantics, though we make an effort to present the system as if it were purely a proof-theoretic construction.

Deverbal Nouns in Knowledge Representation

Deverbal nouns pose serious challenges for knowledge-representation systems. We present a method of canonicalizing deverbal noun representations, relying on a rich lexicon of verb subcategorization frames, the WordNet database, a large finite-state network for derivational morphology and a series of heuristics for mapping deverbal arguments onto the arguments of corresponding verbs.1

Intuitionistic Hybrid Logic

In this chapter we introduce intuitionistic hybrid logic and its proof-theory. Intuitionistic hybrid logic is hybrid modal logic over an intuitionistic logic basis instead of a classical logical basis. The chapter is structured as follows. In the first section of the chapter we introduce intuitionistic hybrid logic (this is taken from Brauner and de Paiva (2006)). In the second section we introduce a natural deduction system for intuitionistic hybrid logic (taken from Brauner and de Paiva (2006)) and in the third and fourth sections we introduce axiom systems for intuitionistic and paraconsistent hybrid logic (taken from Brauner and de Paiva (2006)). In the last section we discuss certain other work, namely a Curry-Howard interpretation of intuitionistic hybrid logic.

Precision-focused Textual Inference

This paper describes our system as used in the RTE3 task. The system maps premise and hypothesis pairs into an abstract knowledge representation (AKR) and then performs entailment and contradiction detection (ECD) on the resulting AKRs. Two versions of ECD were used in RTE3, one with strict ECD and one with looser ECD.

Preventing existence

We discuss the treatment of prevention statements in both naturallanguage semantics and knowledge representation, with particularregard to existence entailments. First order representations withan explicit existence predicate are shown to not adequately capturethe entailments of prevention statements. A linguistic analysis isframed in a higher order intensional logic, employing a Fregeannotion of existence as instantiation of a concept. We discuss howthis can be mapped to a Cyc style knowledge representation.

Natural deduction and context as (constructive) modality

This note describes three formalized logics of context and their mathematical inter-relationships. It also proposes a Natural Deduction formulation for a constructive logic of contexts, which is what the described logics have in common.