Andrea Masini

A Computational Interpretation of Modal Proofs

Proof theory of modal logics, though largely studied since the fifties, has always been a delicate subject, the main reason being the apparent impossibility to obtain elegant, natural systems for intensional operators (with the excellent exception of intuitionistic logic). For example Segerberg, not earlier than 1984 [5], observed that the Gentzen format, which works so well for truth functional and intuitionistic operators, cannot be a priori expected to remain valid for modal logics; carrying to the limit this observation one could even assert that ‘logics with no good proof theory are unnatural.’ In such a way we should mark as ‘unnatural’ all modal logics (with great delight of a large number of logicians!).

On the fine structure of the exponential rule

We present natural deduction systems for fragments of intuitionistic linear logic obtained by dropping weakening and contractions also on !-preexed formulas. The systems are based on a two-dimensional generalization of the notion of sequent, which accounts for a clean formulation of the introduction/elimination rules of the modality. Moreover, the diierent subsystems are obtained in a modular way, by simple conditions on the elimination rule for !. For the proposed systems we introduce a notion of reduction and we prove a normalization theorem.

Parsing MELL Proof Nets

We propose a new formulation for full (weakening and constants included) multiplicative and exponential (MELL) proof nets, allowing a complete set of rewriting rules to parse them. The recognizing grammar defined by such a rewriting system (confluent and strong normalizing on the new proof nets) gives a correctness criterion that we show equivalent to the Danos-Regnier one.

An approach to infinitary temporal proof theory

Abstract.Aim of this work is to investigate from a proof-theoretic viewpoint a propositional and a predicate sequent calculus with an ω–type schema of inference that naturally interpret the propositional and the predicate until–free fragments of Linear Time Logic LTL respectively. The two calculi are based on a natural extension of ordinary sequents and of standard modal rules. We examine the pure propositional case (no extralogical axioms), the propositional and the first order predicate cases (both with a possibly infinite set of extralogical axioms). For each system we provide a syntactic proof of cut elimination and a proof of completeness.

Proof nets, garbage, and computations

We study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic (MELL) proof nets. The main novelty is in a complete set of rewriting rules for cut-elimination in presence of weakening (which requires garbage collection). The proposed reduction system is strongly normalizing and confluent.

Coherence for Sharing Proof Nets

Sharing graphs are a way of representing linear logic proof-nets in such a way that their reduction never duplicates a redex. In their usual presentations, they present a problem of coherence: if the proof-net N reduces by standard cut-elimination to N′, then, by reducing the sharing graph of N we do not obtain the sharing graph of N′. We solve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule (absorption). The rewriting system is confluent and terminating.

An analysis of (linear) exponentials based on extended sequents

We apply the sequents approach to the analysis of several logics derived from linear logic In particular we present a uniform formal system for Linear Logic Elementary Linear Logic and Light Linear Logic

Analysis of Multiresolution-Based Fusion Strategies for a Dual Infrared System

A dual infrared system to assist a driver in bad visibility conditions is studied. The problem of selecting the best multiresolution-based image fusion technique is addressed with reference to automotive scenarios. A new method for objective evaluation of multisensor image fusion strategies is presented for the optimal design of the fusion process. Multiresolution-based fusion methodologies are compared, and experimental results obtained from a prototype dual infrared camera system are shown and analyzed. Numerical results, in terms of the quality of the fused images and of the computational load, are presented and discussed. The effectiveness of the dual infrared system in urban and extraurban automotive scenarios is illustrated with a number of examples.

Sight enhancement through video fusion in a surveillance system

In this paper we consider the problem of fusing two video streams acquired by an RGB camera and a sensor operating in the long wave infrared (LWIR). The application of interest is area surveillance and the fusion process aims at enhancing the human perception of the monitored scene. We propose a fusion procedure where the background and the moving objects are separated and fused by means of different strategies. With respect to standard video fusion techniques this approach has the advantage of reducing the computational load and mitigating the rapid brightness variations in the fused video. It is also less sensitive to the presence of noise. We discuss the experimental results obtained on a typical area surveillance scenario and demonstrate the effectiveness of the proposed method. For this purpose, the analysis is carried out both subjectively, in terms of visual quality of the fused video stream and objectively, in terms of standard image quality indexes. The computational load is also evaluated.

A modal view of linear logic

We present a sequent calculus for the modal logic S4 , and building on some relevant features of this system (the absence of contraction rules and the confinement of weakenings into axioms and modal rules) we show how S4 can easily be translated into full prepositional linear logic, extending the Grishin-Ono translation of classical logic into linear logic. The translation introduces linear modalities (exponentials) only in correspondence with S4 modalities. We discuss the complexity of the decision problem for several classes of linear formulas naturally arising from the proposed translations.