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eventi seminar

Talk by Rineke Verbrugge on May 30th

The last talk of our Lunch Seminar series for this semester will take place on Monday, May 30th at 13:00 and will be given by Rineke Verbrugge ( University of Gronigen)

Title: Every formula of provability logic is either almost always valid or almost always invalid

Abstract:

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. For modal logics, limit behavior for models and frames may differ. In 1994, Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5. They also proposed zero-one laws for the corresponding classes of frames, but their zero-one law for K-frames has since been disproved.

In this talk, we prove zero-one laws for provability logic with respect to both model and frame validity. Moreover, we axiomatize validity in almost all irreflexive transitive finite models and in almost all irreflexive transitive finite frames, leading to two different axiom systems. In the proofs, we use a combinatorial result by Kleitman and Rothschild about the structure of almost all finite partial orders. On the way, we also show that a previous result by Halpern and Kapron about the axiomatization of almost sure frame validity for S4 is not correct.

The talk is based on the following paper: Verbrugge, R. (2021). Zero-one laws for provability logic: Axiomatizing validity in almost all models and almost all frames. In L. Libkin, ed., Proceedings 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (pp. 1-13). IEEE Press.

The Zoom link is available upon request at logic.unimi@gmail.com

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eventi seminar

Talk by Ole Hjortland on May 23rd

The talk by Ole Hjortland ( University of Bergen) for our Lunch Seminar series, originally planned for May 2nd, will take place on Monday, May 23rd at 13:00!

Title: Logical pluralism and abductivism in logic

Abstract:

Logical knowledge has often been considered exceptional, either because it is a priori, foundational, or simply self-evident. Against this, some anti-exceptionalists argue that knowledge of basic logical laws is not acquired via direct access, but through methods of theory choice (e.g., logical abductivism). Here I investigate what such an epistemology of logic will mean for the debate between the logical monist and the logical pluralist. If theory-choice in logic is indeed broadly abductive, does that leave room for the pluralist thesis that there is more than one correct logic? I argue that abductivism might support a form of local pluralism, but that global pluralism is problematic.

The Zoom link is available upon request at logic.unimi@gmail.com

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eventi seminar

Talk by Felix Weitkämper

Our Lunch Seminar series continues on Monday, May 16th! Our speaker will be Felix Weitkämper( LMU Munich) who will give a talk on Statistical relational artificial intelligence and first-order logics of probability

Abstract:

After a general introduction to both components of the title, we will see how the lens of first-order logics of probability can suggest approaches to two interlinked problems in statistical relational AI, both of which have recently garnered much attention in the field:

(1) How can one apply statistical relational methods on large domains given the high complexity of learning and inference?

(2) How can parameters learned on one domain be transferred to a domain of different size?

(*) How can one reconcile these priorities with expressivity and a natural syntax and semantics?

The Zoom link is available upon request at logic.unimi@gmail.com

Categories
eventi seminar

Talk by Ole Hjortland (Postponed, TBD)

N.B. The talk has been postponed, to a date yet to be decided.

Our Lunch Seminar series continues on Monday, May 2nd! Our speaker will be Ole Hjortland ( University of Bergen) who will give a talk on Logical pluralism and abductivism in logic.

Abstract:

Logical knowledge has often been considered exceptional, either because it is a priori, foundational, or simply self-evident. Against this, some anti-exceptionalists argue that knowledge of basic logical laws is not acquired via direct access, but through methods of theory choice (e.g., logical abductivism). Here I investigate what such an epistemology of logic will mean for the debate between the logical monist and the logical pluralist. If theory-choice in logic is indeed broadly abductive, does that leave room for the pluralist thesis that there is more than one correct logic? I argue that abductivism might support a form of local pluralism, but that global pluralism is problematic.

The Zoom link is available upon request at logic.unimi@gmail.com

Categories
eventi seminar

Talk by Alberto Termine

Our Lunch Seminar series continues on Monday, April 11th! Our speaker will be Alberto Termine ( University of Milan) who will give a talk on Model Checking Stochastic Multi Agent Systems with Imprecise Probabilities.

See below for more information and the abstract:

Abstract:

Stochastic multi-agent systems raise the necessity to extend probabilistic model checking to the epistemic domain. Results in this direction have been achieved by epistemic extensions of Probabilistic Computation Tree Logic and related Probabilistic Interpreted Systems. The latter, however, require the probabilities governing the system’s behaviour to be fully specified. As a consequence, neither non-stationary stochastic systems nor systems whose stochastic behaviour is not fully knowable can be treated. Almost all approaches proposed to overcome this limitation require exponential complexity of the checking procedures in the number of states of the model. The theory of imprecise probabilities offers a natural way out. In this paper, we use it to introduce a formalism suitable to model-check multi-agent systems with either a non-stationary or not fully knowable probabilistic behaviour. To this aim, we introduce imprecise probabilistic interpreted systems and present the logical language EIPCTL to specify their properties. Later, we propose an extension of these models based on the introduction of state-rewards and introduce proper operators to specify rewards-related inferences. Finally, we present appropriate model-checking procedures for both cases.

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eventi seminar

Talk by Elaine Pimentel

Our Lunch Seminar series continues on Monday, April 4th! We will host Elaine Pimentel (UCL London) who will give a talk on Ecumenical systems: from natural deduction with stoup to pure modal systems.

See below for more information and the abstract:

Abstract: Natural deduction systems, as proposed by Gentzen and further studied by Prawitz, is one of the most well known proof-theoretical frameworks. Part of its success is based on the fact that natural deduction rules present a simple characterization of logical constants, especially in the case of intuitionistic logic. However, there has been a lot of criticism on extensions of the intuitionistic set of rules in order to deal with classical logic. Indeed, most of such extensions add, to the usual introduction and elimination rules, extra rules governing  negation. As a consequence, several meta-logical properties, the most prominent one being harmony, are lost.

In 2015, Dag Prawitz proposed a natural deduction ecumenical system, where classical logic and intuitionistic logic are codified in the same system. In this system, the classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation and the constant for the absurd, but they would each have their own existential quantifier, disjunction and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantic framework that can be accepted by both parties.  

In this talk, we propose a different approach adapting, to the natural deduction framework,  Girard’s mechanism of stoup.  This will allow the definition of a pure harmonic natural deduction system for the propositional fragment of  Prawitz’ ecumenical logic.

We then show how to extend these ideas to modalities in the sequent calculus presentation.

This is a joint work with Luiz Carlos Pereira, Sonia Marin and Emerson Sales. 

Zoom link:  https://us02web.zoom.us/j/81225169037?pwd=NWRCWU5GeVNLcnZ4VmlmakZldm0yQT09

Categories
eventi seminar

Talk by Ekaterina Kubyshkina

Our Lunch Seminar series continues on Monday, March 21st! We will host Ekaterina Kubyshkina (University of Campinas) who will give a talk on Ignorance as an excuse, formally See below for more information and the abstract:

Abstract. In the current literature on epistemology there is a lively debate on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never considered or thought about a true proposition p. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis was provided for ignorance as an excuse. First, we will argue that if ignorance is expressed via standard modalities of knowledge and belief, one is unable to represent ignorance as an excuse. Secondly, we fill this gap by providing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which ignorance is expressed as a primitive modality. Semantically, the logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, in order to consider the conditions of a possible change of an agent’s ignorance, we will extend the setting by considering public announcements.

Zoom Link: https://us02web.zoom.us/j/81529942850?pwd=VC8vNHRhVkhIUmpKYXBTRGhUdEFZUT09

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eventi seminar

Giuseppe Sergioli’s talk

Our Lunch Seminar series continues on Monday, March 7! We will host Giuseppe Sergioli (University of Cagliari) who will give a talk on Quantum Information and Machine Learning. From foundations to real applications See below for more information and the abstract:

Abstract. This talk is about the connection between quantum in-
formation theory and machine learning. In particular, we show how quantum state discrimination can represent a useful tool to address the standard classification problem in machine learning. We show how the optimal quantum measurement theory developed in the context of quantum information theory and quantum communication can inspire a new binary classification algorithm that can achieve higher inference accuracy for various datasets. Here we also propose a model for arbitrary multiclass classification inspired by quantum state discrimination, which is enabled by encoding the data in the space of linear operators on a Hilbert space. We also show a full comparison between quantum inspired and other standard classifiers over artificial and real datasets.

Zoom Link: https://us02web.zoom.us/j/87689834064?pwd=M08wdWVOa1l6R2thME1aUjRvTDhUdz09

Categories
eventi seminar

Francesca Toni’s seminar

Our Lunch Seminar series re-starts on Monday, February 21! We will host Francesca Toni (Imperial College London) who will give a talk on Argument graphs and assumption-based argumentation. See below for more information and the abstract:

Abstract:

Arguments in structured argumentation are usually defined as trees, and extensions as sets of such tree-based arguments with various properties
depending on the particular argumentation semantics. However, these arguments and extensions may have redundancies as well as circularities, which are conceptually and computationally undesirable. Focusing on the specific case of Assumption-Based Argumentation (ABA), we propose novel notions of arguments and admissible/grounded extensions, both defined in terms of graphs.
We show that this avoids the redundancies and circularities of standard accounts, and set out the relationship to standard tree-based arguments and admissible/grounded extensions (as sets of arguments).

Zoom Link: https://us02web.zoom.us/j/84657174928?pwd=c2lFS2w4RXBUUTNFZ216WGYrakV0UT09

Categories
seminar

Richard Booth’s Seminar

Tomorrow we will have our last LUCI Lunch Seminar before the break! Starting from 1 PM CET, Richard Booth from the University of Cardiff will give a talk on Conditional Inference under Disjunctive Rationality. Please find the link and more information below:

Title: Conditional Inference under Disjunctive Rationality

Abstract: The question of conditional inference, i.e., of which conditional sentences of the form “if α then, normally, β” should follow from a set KB of such sentences, has been one of the classic questions of AI, with several well-known solutions
proposed. Perhaps the most notable is the rational closure construction of Lehmann and Magidor, under which the set of inferred conditionals forms a rational consequence relation, i.e., satisfies all the rules of preferential reasoning, plus Rational Monotonicity. However, this last named rule is not universally accepted, and other researchers have advocated working within the larger class of disjunctive consequence relations, which satisfy the weaker requirement of Disjunctive Rationality. While there are convincing arguments that the rational closure forms the “simplest” rational consequence relation extending a given set of conditionals, the question of what is the simplest disjunctive consequence relation has not been explored. In this talk, we propose a solution to this question and explore some of its properties. (This is joint work with Ivan Varzinczak.)

Zoom Link: https://us02web.zoom.us/j/87116795155