publications

2023

1. AAMAS 2023

   A Deontic Logic of Knowingly Complying Areces, C., Cassano, V., Castro, P., Fervari, R., and Saravia, A. In Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems. Eds.: Agmon, N., An, B., Ricci, A., and Yeoh, W. pp. 364–372. ACM. [Abstract] [PDF]

   We introduce a logic for representing the deontic notion of knowingly complying associated to an agent’s conciousness of taking a normative course of action for achieving a certain goal. Our logic features an operator for describing normative courses of actions, and another operator for describing what each agent knowingly complies with. We provide a sound and complete axiom system for our logic, and study the computational complexity of its satisfiability problem. Finally, we extend our logic with an additional operator for capturing the general abilities of the agents. This operator enables us to distinguish ’what agents can do’ and ’what agents do according to norms’. For this extension, we also provide a sound and complete axiom system.

2022

1. JLC 2022

   Algebraic tools for default modal systems Cassano, V., Fervari, R., Areces, C., and Castro, P. Journal of Logic and Computation [Abstract] [PDF]

   Default Logics are a family of non-monotonic formalisms having so-called defaults and extensions as their common foundation. Traditionally, default logics have been defined and dealt with via syntactic notions of consequence in propositional or first-order logic. Here, we build default logics on modal logics. First, we present these default logics syntactically. Then, we elaborate on an algebraic counterpart. More precisely, we extend the notion of a modal algebra to accommodate for defaults and extensions. Our algebraic view of default logics concludes with an algebraic completeness result and a way of comparing default logics borrowing ideas from the concept of bisimulation in modal logic. To our knowledge, this take on default logics approach is novel. Interestingly, it also lays the groundwork for studying default logics from a dynamic logic perspective.

2. WoLLIC 2022

   Nonmonotonic Reasoning via Dynamic Consequence Areces, C., Cassano, V., and Fervari, R. In 28th Workshop on Logic, Language, Information, and Computation. Eds.: Ciabattoni, A., Pimentel, E., and Queiroz, R. Vol.: 13468. LNCS. pp. 395–410. Springer. [Abstract] [PDF]

   We approach the concept of Pivotal Rule Consequence (𝖯𝖱𝖢) from a semantical perspective, resorting to model updates in Public Announcement Logic (𝖯𝖠𝖫). In doing this, we take inspiration from the notion of dynamic consequence. Our perspective gains in interest since 𝖯𝖱𝖢 serves as a “bridge” from Classical Logic to Default Logic –one of the most well-known non-monotonic formalisms. We show how the internalization of 𝖯𝖱𝖢 in 𝖯𝖠𝖫 leads to clear semantics of the former, and to completeness and transfer results. Moreover, we address the case of credulous consequence in Default Logic as a particular case of 𝖯𝖱𝖢. Interestingly, we cast credulous consequence as a model checking problem. We argue that our results open the way to use well-known semantic tools from modal logic to study properties of different non-monotonic logics.

2021

1. DEON 2020/21

   Deontic Action Logics via Algebra Castro, P., Cassano, V., Fervari, R., and Areces, C. In 15th International Conference on Deontic Logic and Normative Systems. Eds.: Liu, F., Marra, A., Portner, P., and Van De Putte, F. pp. 17. College Publications. [Abstract] [URL] [PDF]

   Deontic logics are dubbed the logics of normative or prescriptive reasoning. These logics can roughly be categorized into ought-to-be, dealing with the prescription of state of affairs, or ought-to-do, dealing with the prescription of actions. An important family of ought-to-do deontic logics have their origin in Segerberg’s Deontic Action Logic (DAL). In this work, we provide an algebraic characterization of DAL and some known variants. In brief, we capture actions and formulas as elements of different base algebras, and deontic operators as algebraic operations; different algebras capture the different variants. This algebraization enables us to obtain completeness results via standard algebraic means. Moreover, we argue that this algebraic framework offers a natural way of (re-)thinking many deontic logical issues at large.

2020

1. DaLi 2020

   Default Modal Systems as Algebraic Updates Cassano, V., Fervari, R., Areces, C., and Castro, P. In 3rd Workshop on Dynamic Logic: New Trends and Applications. Eds.: Martins, M., and Sedlar, I. Vol.: 12569. LNCS. pp. 103–119. Springer. [Abstract] [URL] [PDF]

   Default Logic refers to a family of formalisms designed to carry out non-monotonic reasoning over a monotonic logic (in general, Classical First-Order or Propositional Logic). Traditionally, default logics have been defined and dealt with via syntactic consequence relations. Here, we introduce a family of default logics defined over modal logics. First, we present these default logics syntactically. Then, we elaborate on an algebraic counterpart. We do the latter by extending the notion of a modal algebra to acommodate for the main elements of default logics: defaults and extensions. Our algebraic treatment of default logics concludes with an algebraic completeness result. To our knowledge, our approach is novel, and it lays the groundwork for studying default logics from a dynamic logic perspective.

2019

1. CADE 2019

   A Tableaux Calculus for Default Intuitionistic Logic Cassano, V., Fervari, R., Hoffmann, G., Areces, C., and Castro, P. In 27th International Conference on Automated Deduction. Eds.: Fontaine, P. Vol.: 11716. LNCS. pp. 161–177. Springer. [Abstract] [URL] [PDF]

   We build a Default Logic variant on Intuitionistic Propositional Logic and develop a sound, complete, and terminating, tableaux calculus for it. We also present an implementation of the calculus. We motivate and illustrate the technical elements of our work with examples.

2. JELIA 2019

   Interpolation and Beth Definability in Default Logics Cassano, V., Fervari, R., Areces, C., and Castro, P. In 16th European Conference on Logics in Artificial Intelligence. Eds.: Calimeri, F., Leone, N., and Manna, M. Vol.: 11468. LNCS. pp. 675–691. Springer. [Abstract] [URL] [PDF]

   We investigate interpolation and Beth definability in default logics. To this end, we start by defining a general framework which is sufficiently abstract to encompass most of the usual definitions of a default Logic. In this framework a default logic DL is built on a base, monotonic, logic L. We then investigate the question of when interpolation and Beth definability results transfer from L to DL. This investigation needs suitable notions of interpolation and Beth definability for default logics. We show both positive and negative general results: depending on how DL is defined and of the kind of interpolation/Beth definability involved, the property might or might not transfer from L to DL.

3. TARK 2019

   An Algebraic Approach for Action Based Default Reasoning Castro, P., Cassano, V., Fervari, R., and Areces, C. In 17th Conference on Theoretical Aspects of Rationality and Knowledge. Eds.: Moss, L. Vol.: 297. EPTCS. pp. 91–105. Open Publishing Association. [Abstract] [URL] [PDF]

   Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous computing systems where decisions must be taken in the presence of an incomplete set of norms regulating a particular scenario. Combining default and deontic reasoning over actions allows us to formally reason about such assumptions. With this in mind, we propose a logical formalism for default reasoning over a deontic action logic. The novelty of our approach is twofold. First, our formalism for default reasoning deals with actions and action operators, and it is based on a deontic action logic originally proposed by Segerberg. Second, inspired by Segerberg’s approach, we use tools coming from the theory of Boolean Algebra. These tools allow us to extend Segerberg’s algebraic completeness result to the setting of Default Logics.

2018

1. LPAR-22

   Reasoning About Prescription and Description Using Prioritized Default Rules Cassano, V., Areces, C., and Castro, P. In 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning. Eds.: Barthe, G., Sutcliffe, G., and Veanes, M. Vol.: 57. EPiC Series in Computing. pp. 196–213. EasyChair. [Abstract] [URL] [PDF]

   In this paper we introduce a prioritized default logic. We build this logic modularly from Standard Deontic Logic by the addition of default rules and priorities among them. Our main aim is to provide a logical framework to reason about scenarios where prescriptive and descriptive statements coexist and may be incomplete and contradictory. We motivate and illustrate the technical elements of our work with the use of examples (classical, and coming from software engineering). In addition, we present sound, complete, and terminating (with loop check) tableau-based proof calculi for credulous and sceptical reasoning in our logic.