Reuse and integration of specification logics: the hybridisation perspective

Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. It also captures the construction of first-order encodings of such hybridised institutions into theories in first-order logic. The method was originally developed to build suitable logics for the specification of reconfigurable software systems on top of whatever logic is used to describe local requirements of each system’s configuration. Hybridisation has, however, a broader scope, providing a fresh example of yet another development in combining and reusing logics driven by a problem from Computer Science. This paper offers an overview of this method, proposes some new extensions, namely the introduction of full quantification leading to the specification of dynamic modalities, and exemplifies its potential through a didactical application. It is discussed how hybridisation can be successfully used in a formal specification course in which students progress from equational to hybrid specifications in a uniform setting, integrating paradigms, combining data and behaviour, and dealing appropriately with systems evolution and reconfiguration.This work is financed by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme, and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within project POCI-01-0145-FEDER-006961. M. Martins was further supported by project UID/MAT/04106/2013. A. Madeira and R. Neves research was carried out in the context of a post-doc and a Ph.D. grant with references SFRH/BPD/103004/2014 and SFRH/BD/52234/2013, respectively. L.S. Barbosa is also supported by SFRH/BSAB/ 113890/2015

A Game of Pawns

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its next location. This leads to a path in the graph, which determines the winner. Traditionally, the control of vertices is predetermined and fixed. The novelty of pawn games is that control of vertices changes dynamically throughout the game as follows. Each vertex of a pawn game is owned by a pawn. In each turn, the pawns are partitioned between the two players, and the player who controls the pawn that owns the vertex on which the token is located, chooses the next location of the token. Control of pawns changes dynamically throughout the game according to a fixed mechanism. Specifically, we define several grabbing-based mechanisms in which control of at most one pawn transfers at the end of each turn. We study the complexity of solving pawn games, where we focus on reachability objectives and parameterize the problem by the mechanism that is being used and by restrictions on pawn ownership of vertices. On the positive side, even though pawn games are exponentially-succinct turn-based games, we identify several natural classes that can be solved in PTIME. On the negative side, we identify several EXPTIME-complete classes, where our hardness proofs are based on a new class of games called Lock & Key games, which may be of independent interest

Apoio à Definição de Arquiteturas IIoT Inteligentes

As plataformas IIoT (Industrial Internet-of-Things) são um facilitador na transformação digital, no âmbito da indústria 4.0, promovendo a flexibilidade, para uma adaptação mais rápida às necessidades do mercado, e permitindo às organizações ter uma visão clara sobre o seu estado atual. No entanto, as PMEs (Pequenas e Médias Empresas) estão a encontrar dificuldades na mudança para este novo paradigma, devido à falta de: i) recursos qualificados que são necessários para desenvolver e implementar as suas próprias soluções de digitalização; ii) um entendimento claro sobre a reengenharia necessária que envolve a digitalização, na adoção de soluções IIoT, e iii) modelos adequados para a especificação de soluções IIoT orientadas às PMEs. Com intuito de ultrapassar estes desafios, discute-se uma solução numa dupla perspetiva, em que: i) por um lado, procura-se a automatização da especificação das arquiteturas de plataformas IIoT, de acordo com as necessidades específicas do negócio, reduzindo o investimento necessário para desenvolver este tipo de facilitadores I4.0, e; ii) por outro lado, fomentar o entendimento partilhado do IIoT, entre os especialistas do domínio e as organizações, promovendo o envolvimento de ambas as partes neste processo de especificação. Neste contexto, a semântica desempenha um papel importante, permitindo a acomodação do conhecimento multidisciplinar das arquiteturas IIoT num modelo semântico alavancado por capacidades de raciocínio. Esta solução foi avaliada num caso de estudo, em que a arquitetura produzida pela solução foi comparada, em termos de utilidade, com a arquitetura implementada. O resultado foi que a arquitetura produzida correspondia aos requisitos impostos, pelo que esta foi aprovada pelos especialistas do domínio do caso de estudo, validando a solução.IIoT (Industrial Internet-of-Things) platforms are an enabler for the digital transformation in the scope of industry 4.0, promoting flexibility for a faster adjustment to market and allowing organisations to have a clear vision over its current status. However, SMEs (Small and Medium Enterprises) are struggling to shift into this new paradigm, due to the lack of: i) qualified resources needed to develop and implement their digitalization solutions; ii) a clear understanding about the digitalisation reengineering related IIoT adoption, and; iii) suitable models for SME-oriented IIoT solutions specification. In order to overcome these challenges, a solution is discussed within a twofold perspective: i) on one hand, it looks for the automation of the specification of IIoT platform’s architectures, according to the specific business needs, reducing the investment needed to develop these kind of I4.0 digital enablers, and; ii) on the other hand, it fosters a shared understanding of the IIoT between the domain expert’s and the organisations, promoting the involvement of both parties in this specification process. In this context, semantics plays an impacting role, allowing the accommodation of the multidisciplinary knowledge of IIoT architectures in a semantic model leveraged by reasoning capabilities. This solution was evaluated in a case study, where the architecture produced by the solution was compared, utility wise, with the implemented architecture. The result was that the produced architecture matched the imposed requirements, and so, it was approved by the case study’s domain experts, validating the solution

Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions