ILLC-LIRa

illc-lira@list.uva.nl

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LIRa affiliated event: JRC Joint PhD Celebration on 12 September 14:20 (hybrid)
by LIRa Seminar 23 Aug '23

23 Aug '23

Dear all, We would like to draw your attention to the following LIRa affiliated event. On 12 September 2023, the joint research center for Logic at both Tsinghua University and the University of Amsterdam (UvA) will organize a small workshop to celebrate the completion of three new joint PhD theses. The work reported on in these new PhD thesis projects is perfectly aligned with the main mission of the JRC to further broaden the interdisciplinary view of logic. We will take the opportunity in the afternoon of 12 September to celebrate these new achievements and warmly invite all interested researchers and students to attend the event. The celebration event will take place at the ILLC, University of Amsterdam, Science Park on Tuesday, the 12th of September 2023. This event will be held in hybrid format. See http://tsinghualogic.net/JRC/joint-phd-celebration for all further information. To participate, please complete the registration form on the event’s website! Hope to see you there! Our regular LIRa sessions will resume on 7 September. As usual you can find the sessions and speakers that are already confirmed on our website: https://projects.illc.uva.nl/lgc/seminar/ The LIRa team

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LIRa summer session: Joshua Sack (tomorrow, Thursday, 13 July 16:30)
by LIRa Seminar 12 Jul '23

12 Jul '23

Dear all, We will have a special one-time LIRa summer session tomorrow, on Thursday, 13 July 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Joshua Sack (California State University Long Beach) Date and Time: Thursday, July 13th 2023, 16:30-18:00 Venue: ILLC seminar room F1.15 in Science Park 107 and online Title: Relating algebraic quantum logic structures Abstract. Different quantum structures emphasize different aspects of a quantum system, making it easier for us to reason about those emphasized aspects. The original quantum logics are defined on orthomodular lattices, which generalize the orthocomplemented lattice structure of closed linear subspaces of a Hilbert space. These subspaces represent the testable properties of a quantum system and emphasize static properties of a quantum system. Quantales offer a dynamic perspective of a quantum system, and a quantale-module illustrates the effects of quantum actions and may serve as an algebraic semantics for dynamic quantum logics. A complemented quantale augments a quantale with an orthocomplementation-inducing unary operator. This talk discusses two complemented quantales that are each equivalent to complete orthomodular lattices and account for two basic classes of functions of quantum computation: projectors and unitary operators. Hope to see you there! The LIRa team

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LIRa summer session: Joshua Sack (Thursday, 13 July 16:30)
by LIRa Seminar 07 Jul '23

07 Jul '23

Dear all, We will have a one-time LIRa summer session on Thursday, 13 July 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Joshua Sack (California State University Long Beach) Date and Time: Thursday, July 13th 2023, 16:30-18:00 Venue: ILLC seminar room F1.15 in Science Park 107 and online Title: Relating algebraic quantum logic structures Abstract. Different quantum structures emphasize different aspects of a quantum system, making it easier for us to reason about those emphasized aspects. The original quantum logics are defined on orthomodular lattices, which generalize the orthocomplemented lattice structure of closed linear subspaces of a Hilbert space. These subspaces represent the testable properties of a quantum system and emphasize static properties of a quantum system. Quantales offer a dynamic perspective of a quantum system, and a quantale-module illustrates the effects of quantum actions and may serve as an algebraic semantics for dynamic quantum logics. A complemented quantale augments a quantale with an orthocomplementation-inducing unary operator. This talk discusses two complemented quantales that are each equivalent to complete orthomodular lattices and account for two basic classes of functions of quantum computation: projectors and unitary operators. Hope to see you there! The LIRa team

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LIRa session: Amanda Vidal (tomorrow, Thursday, 15 June 16:30) - note room F3.20
by LIRa Seminar 14 Jun '23

14 Jun '23

Dear all, We will have our next LIRa session tomorrow, on Thursday, 15 June 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Amanda Vidal (IIIA - CSIC) Date and Time: Thursday, June 15th 2023, 16:30-18:00 Venue: KdVI seminar room F3.20 in Science Park 107 and online Title: Computability for some modal many-valued logics. Abstract. Modal logic is one of the most developed and studied non-classical logics, yielding a beautiful equilibrium between complexity and expressivity. On the other hand, substructural (and as a particular case, many- valued) logics provide a formal framework to manage vague and resource sensitive information in a very general (and so, adaptable) fashion. Many-valued modal logics, combining the notions of modal operators with logics over richer algebraic structures is a field in ongoing development. While the first publications on the topic can be traced back to some seminal works by Fitting in the 90s, it has been only in the latter years when a more systematic work has been done. In this talk we present some results for these logics, focused on their decidability and axiomatizability, and compare their behaviour to classical modal logics and the corresponding propositional substructural logics. In particular, we exhibit a family of undecidable non-classical (global) modal logics, including two of the three better known fuzzy logics (namely modal expansions of Łukasiewicz and Product logics). Moreover, we will see how we can further exploit undecidability to show that these logics are not even recursively enumerable, thus not being axiomatizable in the usual sense. This contrasts to what happens in their propositional counterparts, and places they nearer to the behavior of the corresponding FO logics (eg. validity in FO [0, 1]L is not R.E. either). Hope to see you there! The LIRa team

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LIRa session: Amanda Vidal (Thursday, 15 June 16:30) NOTE the room F3.20
by LIRa Seminar 09 Jun '23

09 Jun '23

Dear all, We will have our next LIRa session on Thursday, 15 June 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Amanda Vidal (IIIA - CSIC) Date and Time: Thursday, June 15th 2023, 16:30-18:00 Venue: KdVI seminar room F3.20 in Science Park 107 and online Title: Computability for some modal many-valued logics. Abstract. Modal logic is one of the most developed and studied non-classical logics, yielding a beautiful equilibrium between complexity and expressivity. On the other hand, substructural (and as a particular case, many-valued) logics provide a formal framework to manage vague and resource sensitive information in a very general (and so, adaptable) fashion. Many-valued modal logics, combining the notions of modal operators with logics over richer algebraic structures is a field in ongoing development. While the first publications on the topic can be traced back to some seminal works by Fitting in the 90s, it has been only in the latter years when a more systematic work has been done. In this talk we present some results for these logics, focused on their decidability and axiomatizability, and compare their behaviour to classical modal logics and the corresponding propositional substructural logics. In particular, we exhibit a family of undecidable non-classical (global) modal logics, including two of the three better known fuzzy logics (namely modal expansions of Łukasiewicz and Product logics). Moreover, we will see how we can further exploit undecidability to show that these logics are not even recursively enumerable, thus not being axiomatizable in the usual sense. This contrasts to what happens in their propositional counterparts, and places they nearer to the behavior of the corresponding FO logics (eg. validity in FO [0, 1]L is not R.E. either). Hope to see you there! The LIRa team

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LIRa session: Jan Rooduijn (tomorrow, Thursday, 8 June 16:30) NOTE room F3.20
by LIRa Seminar 07 Jun '23

07 Jun '23

Dear all, We will have our next LIRa session tomorrow, on Thursday, 8 June 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Jan Rooduijn (ILLC) Date and Time: Thursday, June 8th 2023, 16:30-18:00 Venue: KdVI seminar room F3.20 in Science Park 107 and online Title: An analytic proof system for common knowledge logic over S5 Abstract. Common knowledge logic (CKL) extends multi-agent epistemic logic by a common knowledge operator. This operator is interpreted as an infinitary conjunction expressing that a statement is true, all agents know that it is true, all agents know that all agents know that it is true, and so forth. Hilbert-style proof systems typically axiomatise the common knowledge operator using an induction axiom. However, the natural adaptation of this axiom to a Gentzen-style rule requires cut. Even worse, it requires cut formulas outside the context of the proof's conclusion, i.e. non-analytic applications of the cut rule. One solution for still obtaining a nice Gentzen-style system is to turn to cyclic proofs, which replace the explicit induction rule by a more implicit mechanism involving infinite branches. Most existing cyclic proof systems are for logics on which no frame conditions are imposed. This is unnatural for CKL, as one usually assumes certain epistemic principles. One popular frame condition, related to the indistinguishability interpretation of knowledge, requires all accessibility relations to be equivalence relations. In other words, one takes a version of CKL based on the modal logic S5. We will call this logic S5-CKL. In this talk, I will present joint work with Lukas Zenger, in which we construct a cyclic proof system for S5-CKL. Because S5 itself already requires analytic applications of the cut rule, our system does as well. However, unlike for the system with an explicit induction rule, analytic applications suffice for our approach. As a consequence, we show that our system admits an optimal procedure for proof search, and therefore for the validity problem of S5-CKL. In the final part of my talk, I will compare our proof system to various other systems, and I will provide some ideas for applications and future work. This talk is based on a paper accepted at AiML 2022. A preprint can be found here: https://staff.fnwi.uva.nl/j.m.w.rooduijn/papers/S5_aiml22.pdf Hope to see you there! The LIRa team

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LIRa session: Jan Rooduijn (Thursday, 8 June 16:30)
by LIRa Seminar 02 Jun '23

02 Jun '23

Dear all, We will have our next LIRa session on Thursday, 8 June 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Jan Rooduijn (ILLC) Date and Time: Thursday, June 8th 2023, 16:30-18:00 Venue: KdVI seminar room F3.20 in Science Park 107 and online Title: An analytic proof system for common knowledge logic over S5 Abstract. Common knowledge logic (CKL) extends multi-agent epistemic logic by a common knowledge operator. This operator is interpreted as an infinitary conjunction expressing that a statement is true, all agents know that it is true, all agents know that all agents know that it is true, and so forth. Hilbert-style proof systems typically axiomatise the common knowledge operator using an induction axiom. However, the natural adaptation of this axiom to a Gentzen-style rule requires cut. Even worse, it requires cut formulas outside the context of the proof's conclusion, i.e. non-analytic applications of the cut rule. One solution for still obtaining a nice Gentzen-style system is to turn to cyclic proofs, which replace the explicit induction rule by a more implicit mechanism involving infinite branches. Most existing cyclic proof systems are for logics on which no frame conditions are imposed. This is unnatural for CKL, as one usually assumes certain epistemic principles. One popular frame condition, related to the indistinguishability interpretation of knowledge, requires all accessibility relations to be equivalence relations. In other words, one takes a version of CKL based on the modal logic S5. We will call this logic S5-CKL. In this talk, I will present joint work with Lukas Zenger, in which we construct a cyclic proof system for S5-CKL. Because S5 itself already requires analytic applications of the cut rule, our system does as well. However, unlike for the system with an explicit induction rule, analytic applications suffice for our approach. As a consequence, we show that our system admits an optimal procedure for proof search, and therefore for the validity problem of S5-CKL. In the final part of my talk, I will compare our proof system to various other systems, and I will provide some ideas for applications and future work. This talk is based on a paper accepted at AiML 2022. A preprint can be found here: https://staff.fnwi.uva.nl/j.m.w.rooduijn/papers/S5_aiml22.pdf Hope to see you there! The LIRa team

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LIRa session: Niccolò Rossi (tomorrow, Thursday, 25 May 16:30)
by LIRa Seminar 24 May '23

24 May '23

Dear all, We will have our next LIRa session tomorrow, on Thursday, 25 May 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Niccolò Rossi (ILLC, University of Amsterdam) Date and Time: Thursday, May 25th 2023, 16:30-18:00 Venue: ILLC seminar room F3.20 in Science Park 107 and online. Title: Disjunctions, topics and grounds Abstract. If Andrea knows that Biden won the last presidential election, they also know that either Biden won the last presidential election, or Biden is a reptilian. This is the response that epistemic logics based on standard Kripke relational semantics provide, which is consistent with the fact that minimally rational agents can perform disjunction introduction. This is not the case in topic-sensitive semantics though. Andrea might not grasp the concept of 'reptilian', and therefore not be able to know any proposition dealing with reptilians. I argue that this requirement is too strong. I keep the idea that topic-grasping is crucial for knowledge, but I weaken the requirement: only grasping some 'minimal topics' of a proposition is needed. I use a theory of logical grounding (Correia, 2014) in order to define which are the minimal grounds of a proposition and define a minimal topic as the topic of a minimal ground. Once this is done, I propose a semantic clause for knowledge that maintains the good features of topic-sensitive semantics while improving its treatment of disjunction. Doing so, I exploit the concept of logical grounding in order to define the minimal parts of a proposition which are relevant truth-wise and topic-wise for the knowledge of such a proposition. Hope to see you there! The LIRa team

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LIRa session: Niccolò Rossi (Thursday, 25 May 16:30)
by LIRa Seminar 19 May '23

19 May '23

Dear all, We will have our next LIRa session on Thursday, 25 May 16:30. This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723) You can find the details of the talk below. Speaker: Niccolò Rossi (ILLC, University of Amsterdam) Date and Time: Thursday, May 25th 2023, 16:30-18:00 Venue: ILLC seminar room F3.20 in Science Park 107 and online. Title: Disjunctions, topics and grounds Abstract. If Andrea knows that Biden won the last presidential election, they also know that either Biden won the last presidential election, or Biden is a reptilian. This is the response that epistemic logics based on standard Kripke relational semantics provide, which is consistent with the fact that minimally rational agents can perform disjunction introduction. This is not the case in topic-sensitive semantics though. Andrea might not grasp the concept of 'reptilian', and therefore not be able to know any proposition dealing with reptilians. I argue that this requirement is too strong. I keep the idea that topic-grasping is crucial for knowledge, but I weaken the requirement: only grasping some 'minimal topics' of a proposition is needed. I use a theory of logical grounding (Correia, 2014) in order to define which are the minimal grounds of a proposition and define a minimal topic as the topic of a minimal ground. Once this is done, I propose a semantic clause for knowledge that maintains the good features of topic-sensitive semantics while improving its treatment of disjunction. Doing so, I exploit the concept of logical grounding in order to define the minimal parts of a proposition which are relevant truth-wise and topic-wise for the knowledge of such a proposition. Hope to see you there! The LIRa team

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LIRa-related event: Reasoning about Responsible Agency in AI (Tuesday 16 May - please register TODAY)
by LIRa Seminar 08 May '23

08 May '23

Dear all, There will be no LIRa session this and next week, but we would like to draw your attention to the following LIRa-related event: *Reasoning about Responsible Agency in AI* As they become increasingly integrated into our lives, autonomous systems are used to execute more and more tasks that have both normative and epistemic relevance. This has led to a growing literature in machine ethics aiming at addressing the question of how to build autonomous systems that can, first, acquire and properly reason about normative and observational information, and, second, use this information to interact with other agents and the environment in a way that is responsible and, at the same time, explainable. The goal of this workshop is to bring together philosophers, logicians, and computer scientists in order to explore these topics from an interdisciplinary perspective. The workshop is associated with the project Responsible Artificial Agency: A Logical Perspective, funded by the RPA Human(e) AI University of Amsterdam. Date: 16 and 17 May 2023 Venue: Doelenzaal (C0.07) in Amsterdam University Library, Singel 425, 1012 WP Amsterdam NOTE: please REGISTER TODAY if you are planning to attend on location Registration: free of charge but required, use this form: https://forms.gle/yF89isYT9ahRM3B26 For all further information, see the workshop website at https://sites.google.com/view/reasoningaboutresponsibility Hope to see you there! The LIRa team

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