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1

On Modalities and Quantifiers

Fitting M.

Fundamenta Informaticae

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2017

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Vol. 156, nr 3/4

297--330

EN

In 1951 in his book An Essay in Modal Logic, Georg Henrik von Wright strongly called attention to the analogies between quantifiers and modal operators. In 1984 I published a paper in Synthese examining the analogy formally. Confession: the presentation in that paper was badly done, and there is a significant (though correctable) error. Its time to repair the damage, present the ideas in a better way, and continue the investigation further. There are natural sublogics of classical first-order logic that are direct analogs of standard, basic modal logics. The behavior of quantifiers can be given a possible world semantics, some analogous to normal models, some to regular models, and some to neighborhood models. The firstorder logics have axiom systems and generally also tableau systems, paralleling those of modal logics. Many have the interpolation property. This gives concrete substance to von Wright’s observations. But then, what is the crucial difference between modal operators and quantifiers? This turns out to be surprising in its simplicity, and leads to an interesting way of looking at the familiar Henkin style completeness proof for first-order logic.

2

A Framework for the Verification of Parameterized Infinite-state Systems

Alberti F., Ghilardi S., Sharygina N.

Fundamenta Informaticae

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2017

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Vol. 150, nr 1

1--24

EN

We present our framework for the verification of parameterized infinite-state systems. The framework has been successfully applied in the verification of heterogeneous systems, ranging from distributed fault-tolerant protocols to programs handling unbounded data-structures. In such application domains, being able to infer quantified invariants is a mandatory requirement for successful results. Our framework differentiates itself from the state-of-the-art solutions targeting the generation of quantified safe inductive invariants: instead of monolitically exploiting a single static analysis technique, it is based on the effective integration of several analysis strategies. The paper targets the description of the engineering strategies adopted for a successful implementation of such an integrated framework, and presents the extensive experimental evaluation demonstrating its effectiveness.

3

O pewnych zastosowaniach eliminacji kwantyfikatorów w robotyce

Szałas A.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

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2006

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nr 1

139--147

PL

Niniejszy wykład zarysowuje w popularyzującym ujęciu wybrane zagadnieniom efektywnego wnioskowania prowadzonego w warunkach, w których mamy do czynienia z wiedzą niepełną, niepewną i silnie zaszumioną, gdy trzeba poradzić sobie ze złej jakości danymi, w tym bieżącymi odczytami pomiarów, obrazami z kamer itp. Wykład jest oparty o rozwiązania opracowane dla potrzeb bezzałogowych helikopterów (rzeczywiście wykonujących loty bezzałogowe w kontrolowanych warunkach poligonowych). W szczególności naszkicowane będą dość subtelne formy wnioskowania wykorzystujące niebanalne techniki logiczne, drastycznie obniżające złożoność wnioskowania w dużej klasie teorii spotykanych w praktyce.

EN

The current lecture provides a popular overview of selected topics concerning efficient reasoning dealing with incomplete and noisy data of bad quality, collected from sensors and video cameras. The lecture is based on solutions worked out for autonomous aerial vehicles and test flights over a rescure training area in Revinge (Sweden). In particular we sketch rather subtle forms of reasoning based on nontrivial logical methods substantially deceasing the complexity of reasoning in a large class of theories applied in practice.