Fuzzy Sets and Formal Logics

The paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics. Our focus is on the historical side of these developments. © 2015 Elsevier B.V. All rights reserved.partial support by the Spanish projects EdeTRI (TIN2012-39348- C02-01) and 2014 SGR 118.Peer reviewe

From Semantic Games to Provability: The Case of Gödel Logic

We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously developed game for Gödel logic with projection operator in Fermüller et al. (in: M.-J. Lesot, S. Vieira, M.Z. Reformat, J.P. Carvalho, A. Wilbik, B. Bouchon-Meunier, and R.R. Yager, (eds.), Information processing and management of uncertainty in knowledge-based systems, Springer, Cham, 2020, pp. 257–270). This game is extended to cover Gödel logic with involutive negations and constants, and then lifted to a provability game using the concept of disjunctive strategies. Winning strategies in the provability game, with and without constants and involutive negations, turn out to correspond to analytic proofs in a version of SeqGZL (A. Ciabattoni, and T. Vetterlein, Fuzzy Sets and Systems 161(14):1941–1958, 2010) and in a sequent-of-relations calculus (M. Baaz, and Ch.G. Fermüller, in: N.V. Murray, (ed.), Automated reasoning with analytic tableaux and related methods, Springer, Berlin, 1999, pp. 36–51) respectively

Neutrality and Many-Valued Logics

In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.Comment: 119 page

Some Remarks on Relations between Proofs and Games

International audienceThis paper aims at studying relations between proof systems and games in a given logic and at analyzing what can be the interest and limits of a game formulation as an alternative semantic framework for modelling proof search and also for understanding relations between logics. In this perspective, we firstly study proofs and games at an abstract level which is neither related to a particular logic nor adopts a specific focus on their relations. Then, in order to instantiate such an analysis, we describe a dialogue game for intu-itionistic logic and emphasize the adequateness between proofs and winning strategies in this game. Finally, we consider how games can be seen to provide an alternative formulation for proof search and we stress on the possible mix of logical rules and search strategies inside games rules. We conclude on the merits and limits of the game semantics as a tool for studying logics, validity in these logics and some relations between them. 2 Proofs and Games In this section, we present a common terminology to present both proof systems and games at a relatively abstract level. Our aim consists in obtaining tools on which bridges can be built between the proof-theoretical approach and the game semantics approach in establishing the (universal) validity of logical formulae. We explain how proofs and games can be viewed as complementary notions. We illustrate how proof trees in calculi correspond to winning strategies in games and vice-versa

An Empirical Evaluation of the Inferential Capacity of Defeasible Argumentation, Non-monotonic Fuzzy Reasoning and Expert Systems

Several non-monotonic formalisms exist in the field of Artificial Intelligence for reasoning under uncertainty. Many of these are deductive and knowledge-driven, and also employ procedural and semi-declarative techniques for inferential purposes. Nonetheless, limited work exist for the comparison across distinct techniques and in particular the examination of their inferential capacity. Thus, this paper focuses on a comparison of three knowledge-driven approaches employed for non-monotonic reasoning, namely expert systems, fuzzy reasoning and defeasible argumentation. A knowledge-representation and reasoning problem has been selected: modelling and assessing mental workload. This is an ill-defined construct, and its formalisation can be seen as a reasoning activity under uncertainty. An experimental work was performed by exploiting three deductive knowledge bases produced with the aid of experts in the field. These were coded into models by employing the selected techniques and were subsequently elicited with data gathered from humans. The inferences produced by these models were in turn analysed according to common metrics of evaluation in the field of mental workload, in specific validity and sensitivity. Findings suggest that the variance of the inferences of expert systems and fuzzy reasoning models was higher, highlighting poor stability. Contrarily, that of argument-based models was lower, showing a superior stability of its inferences across knowledge bases and under different system configurations. The originality of this research lies in the quantification of the impact of defeasible argumentation. It contributes to the field of logic and non-monotonic reasoning by situating defeasible argumentation among similar approaches of non-monotonic reasoning under uncertainty through a novel empirical comparison

Probabilistic Reasoning with Abstract Argumentation Frameworks

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by considering probability assignments on arguments, allowing for a quantitative treatment of formal argumentation. In this paper, we regard the assignment as denoting the degree of belief that an agent has in an argument being acceptable. While there are various interpretations of this, an example is how it could be applied to a deductive argument. Here, the degree of belief that an agent has in an argument being acceptable is a combination of the degree to which it believes the premises, the claim, and the derivation of the claim from the premises. We consider constraints on these probability assignments, inspired by crisp notions from classical abstract argumentation frameworks and discuss the issue of probabilistic reasoning with abstract argumentation frameworks. Moreover, we consider the scenario when assessments on the probabilities of a subset of the arguments are given and the probabilities of the remaining arguments have to be derived, taking both the topology of the argumentation framework and principles of probabilistic reasoning into account. We generalise this scenario by also considering inconsistent assessments, i.e., assessments that contradict the topology of the argumentation framework. Building on approaches to inconsistency measurement, we present a general framework to measure the amount of conflict of these assessments and provide a method for inconsistency-tolerant reasoning

Artificial Intelligence for Small Satellites Mission Autonomy

Space mission engineering has always been recognized as a very challenging and innovative branch of engineering: since the beginning of the space race, numerous milestones, key successes and failures, improvements, and connections with other engineering domains have been reached. Despite its relative young age, space engineering discipline has not gone through homogeneous times: alternation of leading nations, shifts in public and private interests, allocations of resources to different domains and goals are all examples of an intrinsic dynamism that characterized this discipline. The dynamism is even more striking in the last two decades, in which several factors contributed to the fervour of this period. Two of the most important ones were certainly the increased presence and push of the commercial and private sector and the overall intent of reducing the size of the spacecraft while maintaining comparable level of performances. A key example of the second driver is the introduction, in 1999, of a new category of space systems called CubeSats. Envisioned and designed to ease the access to space for universities, by standardizing the development of the spacecraft and by ensuring high probabilities of acceptance as piggyback customers in launches, the standard was quickly adopted not only by universities, but also by agencies and private companies. CubeSats turned out to be a disruptive innovation, and the space mission ecosystem was deeply changed by this. New mission concepts and architectures are being developed: CubeSats are now considered as secondary payloads of bigger missions, constellations are being deployed in Low Earth Orbit to perform observation missions to a performance level considered to be only achievable by traditional, fully-sized spacecraft. CubeSats, and more in general the small satellites technology, had to overcome important challenges in the last few years that were constraining and reducing the diffusion and adoption potential of smaller spacecraft for scientific and technology demonstration missions. Among these challenges were: the miniaturization of propulsion technologies, to enable concepts such as Rendezvous and Docking, or interplanetary missions; the improvement of telecommunication state of the art for small satellites, to enable the downlink to Earth of all the data acquired during the mission; and the miniaturization of scientific instruments, to be able to exploit CubeSats in more meaningful, scientific, ways. With the size reduction and with the consolidation of the technology, many aspects of a space mission are reduced in consequence: among these, costs, development and launch times can be cited. An important aspect that has not been demonstrated to scale accordingly is operations: even for small satellite missions, human operators and performant ground control centres are needed. In addition, with the possibility of having constellations or interplanetary distributed missions, a redesign of how operations are management is required, to cope with the innovation in space mission architectures. The present work has been carried out to address the issue of operations for small satellite missions. The thesis presents a research, carried out in several institutions (Politecnico di Torino, MIT, NASA JPL), aimed at improving the autonomy level of space missions, and in particular of small satellites. The key technology exploited in the research is Artificial Intelligence, a computer science branch that has gained extreme interest in research disciplines such as medicine, security, image recognition and language processing, and is currently making its way in space engineering as well. The thesis focuses on three topics, and three related applications have been developed and are here presented: autonomous operations by means of event detection algorithms, intelligent failure detection on small satellite actuator systems, and decision-making support thanks to intelligent tradespace exploration during the preliminary design of space missions. The Artificial Intelligent technologies explored are: Machine Learning, and in particular Neural Networks; Knowledge-based Systems, and in particular Fuzzy Logics; Evolutionary Algorithms, and in particular Genetic Algorithms. The thesis covers the domain (small satellites), the technology (Artificial Intelligence), the focus (mission autonomy) and presents three case studies, that demonstrate the feasibility of employing Artificial Intelligence to enhance how missions are currently operated and designed