# GroLog Seminar

Logic seminar of the University of Groningen

# TBA

SPEAKER: Pietro Baroni (University of Brescia, Italy)

DATE: 26 March 2020

TIME: 15:15-17:00

PLACE: Bernoulliborg, room 0293

ABSTRACT

TBA

# CIRCULAR PROOFS IN MODAL LOGIC

SPEAKER: Bahareh Afshari (University of Gothenburg and ILLC, University of Amsterdam)

DATE: 18 February 2020

TIME: 15:15-17:00

PLACE: Bernoulliborg, room 0267

ABSTRACT

In this talk we look at (sound) circular reasoning and how it can been formalised as proof systems in their own right. The focus will be on modal logics, ranging from GL to more expressive languages such as the modal mu-calculus. We will further discuss how circular proofs contribute to the development of the theory of fixed point modal logic and mention future avenues of research.

For a related paper, see Afshari, B., & Leigh, G. E. (2017, June). Cut-free completeness for modal mu-calculus. In 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (pp. 1-12). IEEE.

# LOGIC afternoon ON PROVABILITY & DEL

SPEAKERS: Gerard Renardel de Lavalette (University of Groningen) and Hans van Ditmarsch (LORIA)

DATE: 10 December 2019

TIME: 15:15-17:00

PLACE: Bernoulliborg, room 0222

TITLES & ABSTRACTS

Gerard Renardel de Lavalette: The mathematics of provability

Traditionally, the notion of provability is defined in terms of derivations: sequences or tree-like structures consisting of formulae or sequents, satisfying certain conditions involving proof rules. The 'driving force' of derivations usually consists of conditional statements: implications in the object language A -> B, entailments in the metalanguage, e.g. A,B |- A&B, or proof rules involving sequents: e.g. if G |- A and G,B |- C then G, A -> B |- C.

I propose an alternative, more mathematical definition of derivability, capitalizing on the dynamic character of conditional statements. It is based on set-valued functions F : P(EXP) -> P(EXP), where EXP denotes a collection of expressions and P denotes the power set operator. The intended meaning of F is: for every collection E of expressions, E entails every expression A in F(E). So when EXP is a collection of atomic formulae, F represents the Horn sentence

/\ {/\ E -> A | E a subset of EXP, A in F(E) }

Working out this idea in the context of propositional Horn logic leads to a characterization of derivability: F |- G iff is contained in F*, where F* is the Kleene closure of F. It appears that the set-valued functions with the operator .* form a weak kind of Kleene algebra.This leads to an easy proof of completeness and to several results on uniform and polynomial interpolation.

This first experiment with set-valued functions is extended to full Horn logic and its sublogics EQL (equational logic) and CEQL (conditional equational logic). This brings in substitutions: functions that map expressions to expressions by replacing variables by terms. For Horn logic we have F |- G iff G contained in (SC(F))*, where SC(F) is the substitution closure of F. For EQL and CEQL, we get F |- G iff G contained in (SC(F U EAX))* where U denotes union and EAX is the collection of equality axioms. We obtain straightforward completeness results, and a new technique leads to interpolation results for EQL en CEQL.

Hans van Ditmarsch: Dynamic epistemic logic for distributed computing - asynchrony and concurrency

We will present some recent work on asynchrony and concurrency in dynamic epistemic logics (DEL), building on foundations in distributed computing and temporal epistemic logics. Asynchrony can be modelled by reasoning over histories of actions of different length. How to do this in DEL was proposed by [Dégremont, Löwe, Witzel: TARK 2011]. By equivalence relations on protocol-generated forests along different depths of trees, they can identify action histories of different length. More or less strongly related to DEL this was also considered for: gossip protocols [Apt, Grossi, vd Hoek, TARK 2015], logic puzzles [vD, van Eijck, Wu: KR 2010], and for the immediate snapshot algorithm in distributed computing [Goubault, Ledent, Rajsbaum: GandALF 2018]. We will present the last in some detail: Kripke models and action models can be represented as simplicial complexes. Dynamic epistemic logic can then be interpreted on such complexes.

From the perspective of dynamic epistemic logic, a further departure towards distributed computing and asynchrony is to distinguish the sending and receiving of messages, such as the making versus hearing of announcements. Recent proposals are [Knight, Maubert, Schwarzentruber; MSCS 2019] and [Balbiani, vD, Fernandez Gonzalez; ArXiV 2019] (SR 2017). From the latter we will present asynchronous announcement logic. Its axiomatization resembles that of public announcement logic, and the dynamic modalities can also be eliminated. Further research is on (what is known as) concurrent common knowledge.

Finally, how do we model concurrency in DEL? Both true concurrency and intersection concurrency are conceivable. We recall some older work in the area: [vD, vd Hoek, Kooi: AAMAS 2003] and [van Eijck, Sietsma, Wang: JANCL 2011]. The Muddy Children Problem is a joy forever: the action of three muddy children not stepping forward because none of them know whether they are muddy, is always modelled as the public announcement of a conjunction with three conjuncts. Should this not be a concurrent action with three components?

# BELIEFS BASED ON EVIDENCE AND ARGUMENTATION.

SPEAKER: Fernando Velázquez Quesada (ILLC, University of Amsterdam)

DATE: 12 September 2019

TIME: 15:15-17:00

PLACE: Energy Academy building, room 0062

ABSTRACT:

The talk, based on a series of works together with Chenwei Shi and Sonja Smets ("Argument-based Belief in Topological Structures", "Beliefs Based on Evidence and Argumentation"), presents a logical system that combines a topological extension of evidence models ("Justified Belief and the Topology of Evidence") with tools from abstract argumentation theory ("On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games"). The system uses evidence models for representing the information an agent has collected/inferred about which is the real world, and uses abstract argumentation theory for selecting the sets of evidence that defines the agent's beliefs. The talk will focus on the basic ideas of the two involved frameworks, discussing how they are combined to define two types of beliefs, and the properties of the resulting notions.

# Grolog/LIRa Logic afternoon

SPEAKERS: Roberto Ciuni (Philosophy, University of Padova), Karolina Krzyzanowska (ILLC, University of Amsterdam), Louwe Kuijer (Computer Science, University of Liverpool)

DATE: Monday 1 July 2019

TIME: 14:00-17:00 (& later drinks)

PLACE: Room Beta, Faculty of Philosophy, Oude Boteringestraat 52

TITLES & ABSTRACTS:

Roberto Ciuni: Information-based oughts and their interaction with knowledge and belief

In this talk, I present a conditional logic that enables us to reason about information-based oughts and the role they play in decision-theoretical scenarios that crucially involve knowledge and beliefs. Unconditional oughts and beliefs turn to be special cases of their conditional counterparts. The paper proceeds as follows. After providing a bit of background and setup, I introduce the notions of an objective ought and an information-based ought, and we present a maximality-based semantics for them and the doxastic notions we deal with, in the style of Hansson, Board, van Benthem, Baltag and Smets. Finally, I present a complete axiom system for the resulting logic.

Louwe Kuije: Minimal rationality constraints for conditional obligation

A conditional obligation is of the form O(p|q), with the meaning that p is obligatory under the condition that q is true. We can give semantics to this O operator using a preference relation on states, by saying that O(p|q) holds if p is true on all the "best" q states.

But of course that does not fully determine the semantics unless we specify what we mean by a state being one of the "best". There are several options: we could say that a states is "best" if it is maximal (i.e., there is no other state that is strictly preferred) or if it is optimal (i.e., weakly preferred over all other states). Here, we take a different option and say that a state is among the "best" states if it is part of at least one so-called minimal retentive set. Defining "best" in this way leads to a weak logic for O, but we can find contexts where this weak logic is the appropriate choice.

In this talk I will (i) introduce the semantics for O based on minimal retentive sets and give an example, (ii) introduce a sound an complete axiomatization, and discuss how it differs from other axiomatizations of conditional obligations and (iii) briefly discuss the challenges encountered while defining a canonical model for this logic.

Karolina Krzyzanowska: True clauses, false connections, and the limits of pragmatic explanations

It is a common intuition that the antecedent of an indicative conditional should have something to do with its consequent, that they should be somehow connected. However, only very few theories of conditionals do justice to this intuition. In fact, many prominent accounts of indicative conditionals validate the Principle of Conjunctive Sufficiency that allows to infer a conditional from the truth of its antecedent and the consequent. Consequently, many odd conditionals whose antecedents and consequents are not connected at all are rendered true, or highly acceptable, on these accounts. Their proponents tend to dismiss the oddness of such conditionals as a pragmatic phenomenon, outside the scope of interest of a semanticist or a logician. This is not to say that no pragmatic explanations of the oddity of missing-link conditionals have been proposed. In my talk, I will discuss the most salient of these proposals and I will present empirical data that show how they all fail.

# From grammar inference to learning action models. A case for Explainable AI.

SPEAKER: Nina Gierasimczuk (DTU, Copenhagen)

DATE: 6 June 2019

TIME: 15:15-17:00

PLACE: Room Beta, Faculty of Philosophy, Oude Boteringestraat 52

ABSTRACT:

The endeavour of finding patterns in data spans over many different fields, from computational linguistics to self-driving cars. Machine learning is undeniably a great source of progress across the board. In my talk I will resurrect the old way of thinking about learning, along the lines of symbolic artificial intelligence. I will report on a recent work about inferring action models from descriptions of action executions. Such a framework constitutes an informed, reliable and verifiable way of learning, in which the learner can not only classify objects correctly, but can also report on the symbolic representation she bases her conjectures on. It is nice that the ability for AI to “explain itself” in such a way is nowadays a growing demand in the community. My action models are those of Dynamic Epistemic Logic, and the methodology is automata-theoretic in spirit.

The results on DEL action learning model are based on:

Thomas Bolander and Nina Gierasimczuk, Learning to Act: Qualitative Learning of Deterministic Action Models, Journal of Logic and Computation, Volume 28, Issue 2, 6 March 2018, Pages 337-365.

# Interpolating between Riddles, Tableaux and Self-Referential Truth

SPEAKER: Stefan Wintein (Rotterdam)

DATE: 2 May 2019

TIME: 15:15-17:00

PLACE: Aquarium, Faculty of Philosophy, Oude Boteringestraat 52

ABSTRACT: In "On all Strong Kleene Generalizations of Classical Logic" (Wintein 2016) I developed a uniform tableau calculus, the SK calculus, for what I call 'Strong Kleene Generalizations of Classical Logic', a class of logics including familiar ones such as LP, K3, FDE and Exactly True Logic, but also a host of unfamiliar ones. In my talk, I will explain that and how the SK calculus can be motivated from, and is related to, earlier work I did on Raymond Smullyan’s knight-knave riddles and on theories of self-referential truth. I will also explain how the calculus is used in "Interpolation for Dunn-logics and their extensions" (Wintein and Muskens 2017) to define a novel interpolation method for the logics that it characterizes. In a nutshell, I will use the SK calculus to interpolate between different lines of my research in philosophical logic.

# Ockhamism without Molinism

SPEAKER: Jacek Wawer (Kraków)

DATE: 4 April 2019

TIME: 15:15-17:00

PLACE: Room Beta, Faculty of Philosophy, Oude Boteringestraat 52

ABSTRACT: According to Ockhamism some future contingents are true: a true future contingent faithfully represents what will happen in the actual future. It turns out that a simple-minded representation of Ockhamism within the branching-time framework proves to be highly problematic from the semantic perspective. As a response, many branching-time theorists turned to Molinism -- a theory that assigns truth values not only to actual future contingents, but also to counterfactual future contingents. According to Ockhamism the sentence, "The coin will land heads", uttered before the coin toss is true. According to Molinism, even if one does not toss the coin, the sentence "Had I tossed the coin, it would've landed heads" is true. I will first explain that one can address the formal problems of Ockhamism without resorting to Molinism. Then, I present a formal theory that allows for Ockhamism without Molinism. According to this theory, every future contingent is either true or false, while all the counterfactual future contingents are neither true nor false.