Giuseppe Primiero

The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view.

Some computational phenomena rely essentially on pragmatic considerations, and seem to undermine the independence of the specification from the implementation. These include software development, deviant uses, esoteric languages and recent data-driven applications. To account for them, the interaction between pragmatics, epistemology and ontology in computational artefacts seems essential, indicating the need to recover the role of the language metaphor. We propose a User Levels (ULs) structure as a pragmatic complement to the Levels of Abstraction (LoAs)-based structure defining the ontology and epistemology of computational artefacts. ULs identify a flexible hierarchy in which users bear their own semantic and normative requirements, possibly competing with the logical specification. We formulate a notion of computational act intended in its pragmatic sense, alongside pragmatic versions of implementation and correctness.

Current research in Explainable AI includes post-hoc explanation methods that focus on building transparent explaining agents able to emulate opaque ones. Such agents are naturally required to be accurate and trustworthy. However, what it means for an explaining agent to be accurate and trustworthy is far from being clear. We characterize accuracy and trustworthiness as measures of the distance between the formal properties of a given opaque system and those of its transparent explanantes. To this aim, we extend Probabilistic Computation Tree Logic with operators to specify degrees of accuracy and trustworthiness of explaining agents. We also provide a semantics for this logic, based on a multi-agent structure and relative model-checking algorithms. The paper concludes with a simple example of a possible application.

The process of completing, correcting and prioritising specifications is an essential but very complex task for the maintenance and improvement of software systems. The preservation of functionalities and the ability to accommodate changes are main objectives of the software development cycle to guarantee system reliability. Logical theories able to fully model such processes are still insufficient. In this paper we propose a full formalisation of such operations on software systems inspired by the Alchourrón–Gärdenfors–Makinson paradigm for belief revision of human epistemic states. We represent specifications as finite sets of formulas equipped with a priority relation that models functional entrenchment of properties. We propose to handle specification incompleteness through ordered expansion, inconsistency through ordered safe contraction and prioritisation through revision with reordering, and model all three in an algorithmic fashion. We show how the system satisfies basic properties of the AGM paradigm, including Levi’s and Harper’s identities. We offer a concrete example and complexity results for the inference and model checking problems on revision. We conclude by describing resilience and evolvability of software systems based on such revision operators.

In Information Systems development, resilience has often been treated as a non-functional requirement and little or no work is aimed at building resilience in end-users through systems development. The question of how values and resilience (for the end-user) can be incorporated into the design of systems is an on-going research activity in user-centered design. In this paper we evaluate the relation of values and resilience within the context of an ongoing software development project and contribute a formal model of co-design based on a significant extension of Abstract Design Theory. The formal analysis provides a full and clear-cut definition of the co-design space, its objectives and processes. On the basis of both, we provide an abstract definition of resilient system (for the end-user). We conclude that value-sensitive co-design enforces better resilience in end-users.

We present a multi-conclusion natural deduction calculus characterizing the dynamic reasoning typical of Adaptive Logics. The resulting system AdaptiveND is sound and complete with respect to the propositional fragment of adaptive logics based on CLuN. This appears to be the first tree-format presentation of the standard linear dynamic proof system typical of Adaptive Logics. It offers the advantage of full transparency in the formulation of locally derivable rules, a connection between restricted inference-rules and their adaptive counterpart, and the formulation of abnormalities as a subtype of well-formed formulas. These features of the proposed calculus allow us to clarify the relation between defeasible and multiple-conclusion approaches to classical recapture.

Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of the discipline, combining both historical and systematic analyses. The debates this text surveys are among the latest and most urgent ones: the crisis of foundations in mathematics and the birth of the decision problem, the nature of algorithms, the debates on computational artefacts and malfunctioning, and the analysis of computational experiments. By covering these topics, On the Foundations of Computing provides a much-needed resource to contextualize these foundational issues. For practitioners, researchers, and students alike, a historical and philosophical approach such as what this volume offers becomes essential to understand the past of the discipline and to figure out the challenges of its future.

This paper contributes to the computer ethics debate on software ownership protection by examining the ontological, methodological, and ethical problems related to property right infringement that should come prior to any legal discussion. The ontological problem consists in determining precisely what it is for a computer program to be a copy of another one, a largely neglected problem in computer ethics. The methodological problem is defined as the difficulty of deciding whether a given software system is a copy of another system. And the ethical problem corresponds to establishing when a copy constitutes, or does not constitute, a property right infringement. The ontological problem is solved on the logical analysis of abstract machines, and the latter are argued to be the appropriate level of abstraction for software at which the methodological and the ethical problems can be successfully addressed.

This book presents a systematic philosophical and historical analysis of operating systems (0S). The discussion starts with the evolution of OSs since before their birth. It continues with a comprehensive philosophical analysis grounded in technical aspects. Coverage looks at software and (where appropriate) hardware as well as their historical developments. The authors not only offer historical and philosophical reflections on operating systems. They also explore the programs they coordinate and trace the epsitemic and ontological consequences of their designs. Each chapter investigates one or more overlapping fragments of this fascinating history. These include: the birth of the UNIX system and the development of early systems and prototypes; a conceptual analysis of the plurality of systems; an investigation into business, ethical, and aesthetics aspects related to operating systems; and logical principles of formal languages. This book will interest researchers from a diversity of backgrounds. It will appeal to historians, philosophers, as well as logicians and computer scientists who want to engage with topics relevant to the history and philosophy of programming and more specifically that of operating systems.

The epistemology of computer simulations has become a mainstream topic in the philosophy of technology. Within this large area, significant differences hold between the various types of models and simulation technologies. Agent-based and multi-agent systems simulations introduce a specific constraint on the types of agents and systems modelled. We argue that such difference is crucial and that simulation for the artificial sciences requires the formulation of its own specific epistemological principles. We present a minimally committed epistemology which relies on the methodological principles of the Philosophy of Information and requires weak assumptions on the usability of the simulation and the controllability of the model. We use these principles to provide a new definition of simulation for the context of interest.

Malware has been around since the 1980s and is a large and expensive security concern today, constantly growing over the past years. As our social, professional and financial lives become more digitalised, they present larger and more profitable targets for malware. The problem of classifying and preventing malware is therefore urgent, and it is complicated by the existence of several specific approaches. In this paper, we use an existing malware taxonomy to formulate a general, language independent functional description of malware as transformers between states of the host system and described by a trust relation with its components. This description is then further generalised in terms of mechanisms, thereby contributing to a general understanding of malware. The aim is to use the latter in order to present an improved classification method for malware.

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM c (Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator for bases with partial support.

This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction and elimination rules for modalities are based on the polymorphism of terms in the language. This leads to a multi-modal non-homogeneous version of a type theory, in which we show the embedding of the modal operators into standard group knowledge operators.

This article presents an historical and conceptual overview on different approaches to logical abstraction. Two main trends concerning abstraction in the history of logic are highlighted, starting from the logical notions of concept and function. This analysis strictly relates to the philosophical discussion on the nature of abstract objects. I develop this issue further with respect to the procedure of abstraction involved by (typed) λ-systems, focusing on the crucial change about meaning and predicability. In particular, the analysis of the nature of logical types in the context of Constructive Type Theory allows elucidation of the role of the previously introduced notions. Finally, the connection to the analysis of abstraction in computer science is drawn, and the methodological contribution provided by the notion of information is considered, showing its conceptual and technical relevance. Future research shall focus on the notion of information in distributed systems, analysing the paradigm of information hiding in dependent type theories

Contextual type theories are largely explored in their applications to programming languages, but less investigated for knowledge representation purposes. The combination of a constructive language with a modal extension of contexts appears crucial to explore the attractive idea of a type-theoretical calculus of provability from refutable assumptions for non-monotonic reasoning. This paper introduces such a language: the modal operators are meant to internalize two different modes of correctness, respectively with necessity as the standard notion of constructive verification and possibility as provability up to refutation of contextual conditions.

This paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth in order to connect functional to semantic information, avoiding Gettierization and decoupling from true informational contents. The upgrade operation from functional information uses the machinery of epistemic modalities in order to add data localization and accessibility as its main properties. We show in this way the conceptual worthiness of this notion for issues in contemporary epistemology debates, such as the explanation of knowledge process acquisition from information retrieval systems, and open data repositories.