Towards automating duality

Dualities between different theories occur frequently in mathematics and logic --- between syntax and semantics of a logic, between structures and power structures, between relations and relational algebras, to name just a few. In this paper we show for the case of structures and power structures how corresponding properties of the two related structures can be computed fully automatically by means of quantifier elimination algorithms and predicate logic theorem provers. We illustrate the method with a large number of examples and we give enough technical hints to enable the reader who has access to the {\sc Otter} theorem prover to experiment herself

Logic programming as quantum measurement

The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input) principle is introduced to enhance the resolution of predicate satisfiability problem provided the processor is in a position to perform operations with continuous input. A realization of Zittereingang machine by a quantum system is suggested.Comment: 11 pages, latex, paper accepted for publication in the International Journal of Theoretical Physic

Investigation of DC-8 nacelle modifications to reduce fan-compressor noise in airport communities. Part 5 - Economic implications of retrofit Technical report, May 1967 - Oct. 1969

Economic impact of modifications to DC-8 aircraft nacelles to reduce fan-compressor noise - Part

Tailoring temporal description logics for reasoning over temporal conceptual models

Temporal data models have been used to describe how data can evolve in the context of temporal databases. Both the Extended Entity-Relationship (EER) model and the Unified Modelling Language (UML) have been temporally extended to design temporal databases. To automatically check quality properties of conceptual schemas various encoding to Description Logics (DLs) have been proposed in the literature. On the other hand, reasoning on temporally extended DLs turn out to be too complex for effective reasoning ranging from 2ExpTime up to undecidable languages. We propose here to temporalize the ‘light-weight’ DL-Lite logics obtaining nice computational results while still being able to represent various constraints of temporal conceptual models. In particular, we consider temporal extensions of DL-Lite^N_bool, which was shown to be adequate for capturing non-temporal conceptual models without relationship inclusion, and its fragment DL-Lite^N_core with most primitive concept inclusions, which are nevertheless enough to represent almost all types of atemporal constraints (apart from covering)

Reactive models for biological regulatory networks

A reactive model, as studied by D. Gabbay and his collaborators, can be regarded as a graph whose set of edges may be altered whenever one of them is crossed. In this paper we show how reactive models can describe biological regulatory networks and compare them to Boolean networks and piecewise-linear models, which are some of the most common kinds of models used nowadays. In particular, we show that, with respect to the identification of steady states, reactive Boolean networks lie between piecewise linear models and the usual, plain Boolean networks. We also show this ability is preserved by a suitable notion of bisimulation, and, therefore, by network minimisation.ERDF - The European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947. and project with reference UID/MAT/04106/2019 at CIDMA. D. Figueiredo also acknowledges the support given by FCT via the PhD scholarship PD/BD/114186/201

Algorithmic correspondence and completeness in modal logic. I. The core algorithm SQEMA

Modal formulae express monadic second-order properties on Kripke frames, but in many important cases these have first-order equivalents. Computing such equivalents is important for both logical and computational reasons. On the other hand, canonicity of modal formulae is important, too, because it implies frame-completeness of logics axiomatized with canonical formulae. Computing a first-order equivalent of a modal formula amounts to elimination of second-order quantifiers. Two algorithms have been developed for second-order quantifier elimination: SCAN, based on constraint resolution, and DLS, based on a logical equivalence established by Ackermann. In this paper we introduce a new algorithm, SQEMA, for computing first-order equivalents (using a modal version of Ackermann's lemma) and, moreover, for proving canonicity of modal formulae. Unlike SCAN and DLS, it works directly on modal formulae, thus avoiding Skolemization and the subsequent problem of unskolemization. We present the core algorithm and illustrate it with some examples. We then prove its correctness and the canonicity of all formulae on which the algorithm succeeds. We show that it succeeds not only on all Sahlqvist formulae, but also on the larger class of inductive formulae, introduced in our earlier papers. Thus, we develop a purely algorithmic approach to proving canonical completeness in modal logic and, in particular, establish one of the most general completeness results in modal logic so far.Comment: 26 pages, no figures, to appear in the Logical Methods in Computer Scienc

The k-variable property is stronger than H-dimension k

Accepted versio

Introducing Equational Semantics for Argumentation Networks

This paper provides equational semantics for Dung’s argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the “extensions” of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, etc, etc. The equational approach has its conceptual roots in the 19th century following the algebraic equational approach to logic by George Boole, Louis Couturat and Ernst Schroeder