•  3
    Assisted normative reasoning with Aristotelian diagrams
    with Kathrin Hanauer and Tereza Novotná
    In Giovanni Sileno, Jerry Spanakis & Gijs van Dijck (eds.), Legal Knowledge and Information Systems. Proceedings of JURIX 2023, Ios Press. pp. 89-94. 2023.
    We design a framework for assisted normative reasoning based on Aristotelian diagrams and algorithmic graph theory which can be employed to address heterogeneous tasks of deductive reasoning. Here we focus on two problems of normative determination: we show that the algorithms used to address these problems are computationally efficient and their operations are traceable by humans. Finally, we discuss an application of our framework to a scenario regulated by the GDPR.
  •  9
    Hyperintensional models for non-congruential modal logics
    Logic Journal of the IGPL. forthcoming.
    In this work, we illustrate applications of a semantic framework for non-congruential modal logic based on hyperintensional models. We start by discussing some philosophical ideas behind the approach; in particular, the difference between the set of possible worlds in which a formula is true (its intension) and the semantic content of a formula (its hyperintension), which is captured in a rigorous way in hyperintensional models. Next, we rigorously specify the approach and provide a fundamental …Read more
  •  1
    Allowed, or enabled, that is the question
    with Giovanni Sileno and Réka Markovich
    In Juliano Maranhao, Clayton Peterson, Christian Straßer & Leendert Van der Torre (eds.), Deontic Logic and Normative Systems. Proceedings of DEON 2023, College Publications. pp. 297-317. 2023.
    The formal analysis of normative systems has traditionally focused on their deontic dimension rather than on their potestative dimension; yet, a growing amount of works aims at shedding light on the notion of power, its norm changing potential and its general interactions with deontic concepts. The present article contributes to this line of inquiry by adopting the following perspective: a normative system can be metaphorically seen as an agent that allocates abilities (powers) in order to promo…Read more
  •  5
    This article proposes the use of temporal logic for an analysis of instrumentality inspired by the work of G.H. von Wright. The first part of the article contains the philosophical foundations. We discuss von Wright’s general theory of agency and his account of instrumentality. Moreover, we propose several refinements to this framework via rigorous definitions of the core notions involved. In the second part, we develop a logical system called Temporal Logic of Action and Expectations (TLAE). Th…Read more
  •  4
    A formal, diagrammatic, and operational study of normative relations
    with Giovanni Sileno
    Journal of Logic and Computation 33 (4): 764-795. 2023.
    In this work, we provide an extensive analysis of Hohfeld’s theory of normative relations, focusing in particular on diagrammatic structures. Our contribution is threefold. First, we specify an extensional formal language to represent the main notions in the two families of normative relations identified by Hohfeld (i.e. the deontic and the potestative family). Our primary focus is on the part of the theory concerning potestative relations. In this regard, we assign a key role to the concept of …Read more
  • Permanence vs. termination: a logical analysis
    Logique Et Analyse 257 57-78. 2022.
    The present article is devoted to a logical inquiry on the notions of permanence and termination, which play a central role in many areas of temporal reasoning. In the first part, we introduce a bimodal framework to represent these notions and provide a syntactic and semantic comparison with a monomodal framework representing the notion of future necessity. In the second part, we focus on the problem of defining synonymous logical systems over the two frameworks; as an example, we provide an ext…Read more
  •  8
    Normatively determined propositions
    In V. Giardino, S. Linker, S. Burns, F. Bellucci, J. M. Boucheix & P. Viana (eds.), Diagrammatic Representation and Inference. Proceedings of Diagrams 2022, Springer. pp. 78-85. 2022.
    In the present work we provide a logical analysis of normatively determined and non-determined propositions. The normative status of these propositions depends on their relation with another proposition, here named reference proposition. Using a formal language that includes a monadic operator of obligation, we define eight dyadic operators that represent various notions of “being normatively (non-)determined”; then, we group them into two families, each forming an Aristotelian square of opposit…Read more
  •  52
    Vicarious liability: a solution to a problem of AI responsibility?
    Ethics and Information Technology 24 (3): 1-11. 2022.
    Who is responsible when an AI machine causes something to go wrong? Or is there a gap in the ascription of responsibility? Answers range from claiming there is a unique responsibility gap, several different responsibility gaps, or no gap at all. In a nutshell, the problem is as follows: on the one hand, it seems fitting to hold someone responsible for a wrong caused by an AI machine; on the other hand, there seems to be no fitting bearer of responsibility for this wrong. In this article, we focu…Read more
  •  24
    Generalizing Deontic Action Logic
    Studia Logica 110 (4): 989-1033. 2022.
    We introduce a multimodal framework of deontic action logic which encodes the interaction between two fundamental procedures in normative reasoning: conceptual classification and deontic classification. The expressive power of the framework is noteworthy, since it combines insights from agency logic and dynamic logic, allowing for a representation of many kinds of normative conflicts. We provide a semantic characterization for three axiomatic systems of increasing strength, showing how our appro…Read more
  •  263
    Vicarious responsibility is a notoriously puzzling notion in normative reasoning. In this article we will explore two fundamental issues, which we will call the “explication problem” and the “justification problem”. The former issue concerns how vicarious responsibility can plausibly be defined in terms of other normative concepts. The latter issue concerns how ascriptions of vicarious responsibility can be justified. We will address these two problems by combining ideas taken from legal theory …Read more
  •  20
    An Axiomatic Approach to the Quantified Argument Calculus
    Erkenntnis 88 (8): 3605-3630. 2023.
    The present article employs a model-theoretic semantics to interpret a fragment of the language of the Quantified Argument Calculus (Quarc), a recently introduced logical system whose main aim is capturing the structure of natural language sentences in a closer way than does the language of classical logic. The main contribution is an axiomatization for the set of formulas that are valid in all standard interpretations within the employed semantics.
  •  27
    We provide a fine-grained analysis of notions of regret and responsibility (such as agent-regret and individual responsibility) in terms of a language of multimodal logic. This language undergoes a detailed semantic analysis via two sorts of models: (i) relating models, which are equipped with a relation of propositional pertinence, and (ii) synonymy models, which are equipped with a relation of propositional synonymy. We specify a class of strictly relating models and show that each synonymy mo…Read more
  •  12
    In the present article we exploit the logical notions of correctness and completeness to provide an analysis of some fundamental problems that can be encountered by a software developer when transforming norms for traffic circulation into programming instructions. Relying on this analysis, we then introduce a question and answer procedure that can be helpful, in case of an accident, to clarify which components of an existing framework should be revised and to what extent software developers can …Read more
  •  9
    Computability of diagrammatic theories for normative positions
    with Giovanni Sileno
    In Erich Schweighofer (ed.), Legal Knowledge and Information Systems. Proceedings of JURIX 2021, Ios Press. pp. 171-180. 2021.
    Normative positions are sometimes illustrated in diagrams, in particular in didactic contexts. Traditional examples are the Aristotelian polygons of opposition for deontic modalities (squares, triangles, hexagons, etc.), and the Hohfeldian squares for obligative and potestative concepts. Relying on previous work, we show that Hohfeld’s framework can be used as a basis for developing several Aristotelian polygons and more complex diagrams. Then, we illustrate how logical theories of increasing st…Read more
  •  10
    The search for symmetry in Hohfeldian modalities
    with Giovanni Sileno
    In Amrita Basu, Gem Stapleton, Sven Linker, Catherine Legg, Emmanuel Manalo & Petrucio Viana (eds.), Diagrammatic Representation and Inference. Proceedings of Diagrams 2021, Springer. pp. 87-102. 2021.
    In this work we provide an analysis of some issues arising with geometrical representations of a family of deontic and potestative relations that can be classified as Hohfeldian modalities, traditionally illustrated on two diagrams, the Hohfeldian squares. Our main target is the lack of symmetry to be found in various formal accounts by drawing analogies with the square of opposition for alethic modalities. We argue that one should rather rely on an analogy with the alethic hexagon of opposition…Read more
  •  19
    The good, the bad and the right. Formal reductions among deontic concepts
    Bulletin of the Section of Logic 50 (2): 151-176. 2021.
    The present article provides a taxonomic analysis of bimodal logics of normative ideality and normative awfulness, two notions whose meaning is here explained in terms of the moral values pursued by a given community. Furthermore, the article addresses the traditional problem of a reduction among deontic concepts: we explore the possibility of defining other relevant normative notions, such as obligation, explicit permission and Hohfeldian relations, in terms of ideality and awfulness. Some pr…Read more
  •  18
    The article offers an overview of the deontic theory developed by the philosophical school of Mīmāṃsā, which is, and has been since the last centuries BCE, the main source of normative concepts in Sanskrit thought. Thus, the Mīmāṃsā deontics is interesting for any historian of philosophy and constitutes a thought-provoking occasion to rethink deontic concepts, taking advantage of centuries of systematic reflections on these topics. Some comparison with notions currently used in Euro-American nor…Read more
  •  18
    A bimodal simulation of defeasibility in the normative domain
    with Tomer Libal, Leendert van der Torre, and Dov Gabbay
    In Proceedings of FCR-2020, Ceur Workshop Proceedings. pp. 41-54. 2020.
    In the present work we illustrate how two sorts of defeasible reasoning that are fundamental in the normative domain, that is, reasoning about exceptions and reasoning about violations, can be simulated via monotonic propositional theories based on a bimodal language with primitive operators representing knowledge and obligation. The proposed theoretical framework paves the way to using native theorem provers for multimodal logic, such as MleanCoP, in order to automate normative reasoning.
  •  97
    Normative parties in subject position and in object position
    with Tereza Novotná
    In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2020, College Publications. pp. 147-164. 2021.
    We analyze some normative relations as instances of a general schema of relations among a finite number of parties; in this schema parties can play various roles grouped into two main conceptual layers, called 'subject position' and 'object position'. Relying on the theoretical apparatus introduced, we develop a new symbolic representation for normative reasoning which constitutes an alternative to approaches available in the literature. Our contribution includes a semantic characterization for…Read more
  •  4
    Disentangling deontic positions and abilities: a modal analysis
    with Giovanni Sileno
    In Proceedings of CILC 2020, Ceur Workshop Proceedings. pp. 36-50. 2020.
    Computational systems are traditionally approached from control-oriented perspectives; however, as soon as we move from centralized to decentralized computational infrastructures, direct control needs to be replaced by distributed coordination mechanisms that are on par with institutional constructs observable in human societies (contracts, agreements, enforcement mechanisms, etc.). This paper presents a formalization of Hohfeld's framework building upon a logic whose language includes primitive…Read more
  •  80
    In philosophical logic and metaphysics there is a long-standing debate around the most appropriate structures to represent indeterministic scenarios concerning the future. We reconstruct here such a debate in a computational setting, focusing on the fundamental difference between moment-based and history-based structures. Our presentation is centered around two versions of an indeterministic scenario in which a programmer wants a machine to perform a given task at some point after a specified ti…Read more
  •  22
    Axiomatizing norms across time and the 'Paradox of the Court'
    In Fenrong Liu, Alessandra Marra, Paul Portner & Frederik Van de Putte (eds.), Deontic Logic and Normative Systems. Proceedings of DEON 2020/2021, College Publications. pp. 201-218. 2021.
    In normative reasoning one typically refers to intervals of time across which norms are intended to hold, as well as to alternative possibilities representing hypothetical developments of a given scenario. Thus, deontic modalities are naturally intertwined with temporal and metaphysical ones. Furthermore, contemporary debates in philosophy suggest that a proper understanding of fundamental ethical principles, such as the Ought-Implies-Can thesis, requires a simultaneous analysis of these three f…Read more
  •  13
    A Note on the Issue of Cohesiveness in Canonical Models
    Journal of Logic, Language and Information 29 (3): 331-348. 2020.
    In their presentation of canonical models for normal systems of modal logic, Hughes and Cresswell observe that some of these models are based on a frame which can be also thought of as a collection of two or more isolated frames; they call such frames ‘non-cohesive’. The problem of checking whether the canonical model of a given system is cohesive is still rather unexplored and no general decision procedure is available. The main contribution of this article consists in introducing a method whic…Read more
  •  14
    A realistic view on normative conflicts
    Logic and Logical Philosophy 29 (3): 447-462. 2020.
    Kulicki and Trypuz (2016) introduced three systems of multivalued deontic action logic to handle normative conflicts. The first system suggests a pessimistic view on normative conflicts, according to which any conflicting option represents something forbidden; the second system suggests an optimistic view, according to which any conflicting option represents something obligatory; finally, the third system suggests a neutral view, according to which any conflicting option represents something tha…Read more
  •  8
    Notions of instrumentality in agency logic
    with Kees van Berkel
    In T. Miller, O. Nir, Y. Sakurai, I. Noda, B. T. R. Savarimuthu & S. Tran (eds.), PRIMA 2018: Principles and Practice of Multi-Agent Systems, Springer. pp. 403-419. 2018.
    We present a logic of agency called LAE whose language includes propositional constants for actions and expectations. The logic is based on Von Wright’s theory of agency in general and his analysis of instrumentality in particular. An axiomatization of the logic, including an independence of agents axiom, is provided and soundness and completeness are shown with respect to its intended class of frames. The framework of LAE will allow us to formally define a manifold of concepts involved in agenc…Read more
  •  8
    In this article we introduce a logical structure for normative reasoning, called Normative Detachment Structure with Ideal Conditions, that can be used to represent the content of certain legal texts in a normalized way. The structure exploits the deductive properties of a system of bimodal logic able to distinguish between ideal and actual normative statements, as well as a novel formalization of conditional normative statements able to capture interesting cases of contrary-to-duty reasoning an…Read more
  •  6
    Influence of world knowledge and context on the comprehension of natural language translation of logical formulas
    with Luca Cilibrasi
    In Chiara Ciarlo & Davide Giannoni (eds.), Language Studies Working Papers, University of Reading. pp. 13-21. 2013.
    In this paper we present an approach to conditional reasoning tasks based on two main ideas. The first idea is that, in contrast with what is usually assumed, an ‘if… then…’ sentence is not an adequate translation in natural language of a logical formula containing a material implication as its principal operator. The second idea is that when subjects are required to check the validity of a sentence in a task, their inferences are not driven uniquely by the content of the sentence, but also by o…Read more
  •  11
    Formal analysis of responsibility attribution in a multimodal framework
    In Matteo Baldoni, Mehdi Dastani, Beishui Liao, Yuko Sakurai & Rym Zalila Wenkstern (eds.), PRIMA 2019: Principles and Practice of Multi-Agent Systems, Springer. pp. 36-51. 2019.
    The present article is devoted to a logical treatment of some fundamental concepts involved in responsibility attribution. We specify a theoretical framework based on a language of temporal deontic logic with agent-relative operators for deliberate causal contribution. The framework is endowed with a procedure to solve normative conflicts which arise from the assessment of different normative sources. We provide a characterization result for a basic system within this framework and illustrate ho…Read more
  •  25
    Preface
    Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3): 318-322. 2019.
    Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".
  •  42
    Duty and Sacrifice: A Logical Analysis of the Mīmāṃsā Theory of Vedic Injunctions
    with Elisa Freschi and Andrew Ollett
    History and Philosophy of Logic 40 (4): 323-354. 2019.
    The Mīmāṃsā school of Indian philosophy has for its main purpose the interpretation of injunctions that are found in a set of sacred texts, the Vedas. In their works, Mīmāṃsā authors provide some of the most detailed and systematic examinations available anywhere of statements with a deontic force; however, their considerations have generally not been registered outside of Indological scholarship. In the present article we analyze the Mīmāṃsā theory of Vedic injunctions from a logical and philos…Read more