Probabilistic Argumentation. An Equational Approach

There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: a. the nature of the arguments involved; b. the membership relation in the set S of arguments; c. the attack relation; and d. the choice of extensions. Generically to add a new aspect (probabilistic, or fuzzy, or temporal, etc) to an argumentation network can be done by adding this feature to each component a-d. This is a brute-force method and may yield a non-intuitive or meaningful result. A better way is to meaningfully translate the object system into another target system which does have the aspect required and then let the target system endow the aspect on the initial system. In our case we translate argumentation into classical propositional logic and get probabilistic argumentation from the translation. Of course what we get depends on how we translate. In fact, in this paper we introduce probabilistic semantics to abstract argumentation theory based on the equational approach to argumentation networks. We then compare our semantics with existing proposals in the literature including the approaches by M. Thimm and by A. Hunter. Our methodology in general is discussed in the conclusion

Coalgebras and Their Logics

Transition systems pervade much of computer science. This article outlines the beginnings of a general theory of specification languages for transition systems. More specifically, transition systems are generalised to coalgebras. Specification languages together with their proof systems, in the following called (logical or modal) calculi, are presented by the associated classes of algebras (e.g., classical propositional logic by Boolean algebras). Stone duality will be used to relate the logics and their coalgebraic semantics

Meta SOS - A Maude Based SOS Meta-Theory Framework

Meta SOS is a software framework designed to integrate the results from the meta-theory of structural operational semantics (SOS). These results include deriving semantic properties of language constructs just by syntactically analyzing their rule-based definition, as well as automatically deriving sound and ground-complete axiomatizations for languages, when considering a notion of behavioural equivalence. This paper describes the Meta SOS framework by blending aspects from the meta-theory of SOS, details on their implementation in Maude, and running examples.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Dual-Context Calculi for Modal Logic

We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of assumptions, one of which can be thought as modal, and the other as intuitionistic. We show that these calculi have their roots in in sequent calculi. We then investigate their metatheory, equip them with a confluent and strongly normalizing notion of reduction, and show that they coincide with the usual Hilbert systems up to provability. Finally, we investigate a categorical semantics which interprets the modality as a product-preserving functor.Comment: Full version of article previously presented at LICS 2017 (see arXiv:1602.04860v4 or doi: 10.1109/LICS.2017.8005089

Homogeneous Structures: Model Theory meets Universal Algebra (online meeting)

The workshop "Homogeneous Structures: Model Theory meets Universal Algebra'' was centred around transferring recently obtained advances in universal algebra from the finite to the infinite. As it turns out, the notion of homogeneity together with other model-theoretic concepts like $\omega$-categoricity and the Ramsey property play an indispensable role in this endeavour

Combining Algebra and Higher-Order Types

We study the higher-order rewrite/equational proof systems obtained by adding the simply typed lambda calculus to algebraic rewrite/equational proof systems. We show that if a many-sorted algebraic rewrite system has the Church-Rosser property, then the corresponding higher-order rewrite system which adds simply typed ß-reduction has the Church-Rosser property too. This result is relevant to parallel implementations of functional programming languages. We also show that provability in the higher-order equational proof system obtained by adding the simply typed ß and η axioms to some many-sorted algebraic proof system is effectively reducible to provability in that algebraic proof system. This effective reduction also establishes transformations between higher-order and algebraic equational proofs, transformations which can be useful in automated deduction

Formal Models and Techniques for Analyzing Security Protocols: A Tutorial

International audienceSecurity protocols are distributed programs that aim at securing communications by the means of cryptography. They are for instance used to secure electronic payments, home banking and more recently electronic elections. Given The financial and societal impact in case of failure, and the long history of design flaws in such protocol, formal verification is a necessity. A major difference from other safety critical systems is that the properties of security protocols must hold in the presence of an arbitrary adversary. The aim of this paper is to provide a tutorial to some modern approaches for formally modeling protocols, their goals and automatically verifying them

An Optimizing Protocol Transformation for Constructor Finite Variant Theories in Maude-NPA

[EN] Maude-NPA is an analysis tool for cryptographic security protocols that takes into account the algebraic properties of the cryptosystem. Maude-NPA can reason about a wide range of cryptographic properties. However, some algebraic properties, and protocols using them, have been beyond Maude-NPA capabilities, either because the cryptographic properties cannot be expressed using its equational unification features or because the state space is unmanageable. In this paper, we provide a protocol transformation that can safely get rid of cryptographic properties under some conditions. The time and space difference between verifying the protocol with all the crypto properties and verifying the protocol with a minimal set of the crypto properties is remarkable. We also provide, for the first time, an encoding of the theory of bilinear pairing into Maude-NPA that goes beyond the encoding of bilinear pairing available in the Tamarin toolPartially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grant PROMETEO/2019/098, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286. Julia Sapiña has been supported by the Generalitat Valenciana APOSTD/2019/127 grantAparicio-Sánchez, D.; Escobar Román, S.; Gutiérrez Gil, R.; Sapiña-Sanchis, J. (2020). An Optimizing Protocol Transformation for Constructor Finite Variant Theories in Maude-NPA. 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