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# Representing Knowledge: logical and philosophical approaches

This meeting is organized by the ANR-DFG funded project BEYOND LOGIC. The aim of the conference is to shed new light on epistemological issues related to knowledge representation. More precisely, the conference investigates how to extend logical analysis to extra-logical notions, such as knowledge, ignorance, belief formation and deception, with a particular focus on common knowledge, multi-agency, epistemic logic and many-valued logics.

**Speakers**

- Paul Egré (IJN - ENS)
- Wiebe van der Hoek (University of Liverpool)
- Benjamin Icard (IJN - ENS)
- Manuel Križ (LSCP - ENS)
- Ekaterina Kubyshkina (IHPST - Paris 1)
- Heinrich Wansing (Ruhr University Bochum)

**Program**

9:30 – 10:30 – Wiebe van der Hoek, *Program models and semi-public environments*

10:30 – 10:45 – coffee break

10:45 – 11:30 – Ekaterina Kubyshkina, *Representing ignorance: a truth-functional approach*

11:30 – 12:30 – Paul Egré, *On logical consequence in many-valued logics*

12:30 – 14:30 – lunch

14:30 – 15:30 – Heinrich Wansing, *Three sources of knowledge*

15:30 – 15:45 – coffee break

15:45 – 16:30 – Manuel Križ, *A Trivalent Logic for Plural Predication*

16:30 – 17:15 – Benjamin Icard, *The ‘Surprise Deception Paradox’: a conceptual and logical insight into veridical deception*

**Titles and abstracts**

#### Paul Egré (IJN - ENS)

*On logical consequence in many-valued logics*

*pure consequence*(the preservation of a common set of values from premisses to conclusion) as most familiar from the work of Lukasiewicz and Tarski (viz. Lukasiewicz 1920, Tarski 1930, Hajek 1998); so-called

*mixed consequence*(the inclusion of the premises in some designated set implies the inclusion of the conclusion in some possibly distinct set, as considered in Malinowski 1990, Zardini 2008, Cobreros et al. 2012, Ripley 2013 among others); and

*order-theoretic consequence*(the value of the conclusion should not be less than the infimum of the values of the premisses, as in Machina 1976).

*monotone truth-functional*the class of consequence relations satisfying those properties. Our main result is that the class of monotone truth-functional consequence relations for a many-valued logic coincides exactly with the class of mixed consequence relations and their conjunction - therefore including pure consequence relations and the order-theoretic consequence. We also provide an enumeration of the set of monotone-truth-functional relations in the case of finite many-valued logics based on well-ordered truth values as well as on a particular class of partially ordered truth values.

*good*consequence relation. On the one hand, our result may be seen as insufficiently permissive (because although nonreflexive and nontransitive relations are admitted, nonmonotone relations are not), and on the other as insufficiently restrictive (because a plethora of consequence relations remain when values are partially ordered). We put both problems in perspective and discuss the possibility of including further independent criteria.

#### Wiebe van der Hoek (University of Liverpool)

*Program models and semi-public environments*

#### Benjamin Icard (IJN - ENS)

*The ‘Surprise Deception Paradox’: a conceptual and logical insight into veridical deception*

*deception*(i.e. causing someone to hold a false belief through a false piece of information) by offering epistemic accounts of this pervasive attitude. They have used both conceptual methods [e.g. Chisholm & Feehan 1977; Adler 1997; Mahon 2008] and more formal ones [e.g. Sakama et al. 2010a, 2010b; van Ditmarsch et al. 2012, 2014]. By doing so, however, they have focused on deception caused by false information. But a more subtle form of deception can also happen with the dissemination of true information. We may call

*veridical deception*the method of causing someone to hold a false belief through a true piece of information. Veridical deception has aroused strong interest as well, particularly for those working at the interface with pragmatics on

*double bluff*strategies [e.g. Fallis 2014],

*presupposition failures*[e.g. Harder & Kock 1976; Vincent & Castelfranchi 1981] and

*false implicatures*[e.g. Adler 1997; Fallis 2014].

*publicly announced*that they would do so. Following Baltag and Smets’ treatment of the “Surprise Exam Paradox” [Baltag & Smets, Forthcoming], I will show that this deception paradox raises similar issues. Moreover, I will argue that it can be simply formalized in Dynamic Belief Revision Theory and receive a solution using adequate plausibility orders over a set of possible states.

*true*(he will in fact deceive the addressee), the addressee

*cannot know*that the announcement is true at the time of the announcement (it is not common knowledge among them, for only the deceiver knows that the announcement is true). Nevertheless, the addressee knows something after the announcement: he

*knows*that the deceiver is ‘unreliable’ because the deceiver explicitly states that he is deceitful, so either truthful or untruthful (or both), thus absolutely unpredictable. I aim to show, by model-theoretical means, that the addressee adopts a “belief update” attitude regarding the deceiver’s announcement, which is too strong and results in the paradox. I will define a weaker dynamic attitude which can help resolve the paradox.

#### Manuel Križ (LSCP - ENS)

*A Trivalent Logic for Plural Predication*

#### Ekaterina Kubyshkina (IHPST - Paris 1)

*Representing ignorance: a truth-functional approach*

*Logic for ignorance”*(van der Hoek, Lomuscio, 2004). This work introduces a logic (

*Ig*) in which the I-operator represents the ignorance of an agent. The crucial point of the work is that the I-operator cannot be defined by the K-operator. This result provides a formal basis to challenge the idea that ignorance should be defined in terms of knowledge.

*LRA*), in which the fact of knowing or ignoring some statement is formalized at the level of valuations, without the use of K- or I-operators. On the basis of this semantics, a sound and complete system is provided. Remarkably, the principles for ignorance that we accept in this logic are not dependent on the knowledge principles and vice versa. Thus, ignorance and knowledge in this logic are not inter-definable. In the final part of the talk, a translation from the system

*Ig*to

*LRA*is presented. This translation permits to compare these two logics and clarify the basic principles about the notion of ignorance.

#### Heinrich Wansing (Ruhr University Bochum)

*Three sources of knowledge*

Epistemologists distinguish between different kinds of knowledge, such as a priori knowledge, a posteriori knowledge, testimonial knowledge, perceptual knowledge, inference-based knowledge, etc. The two last-mentioned categories correspond with certain sources of knowledge and kinds of belief acquisition: perception and various forms of inference. In this talk I intend to consider three different sources of knowledge with corresponding methods of belief formation, namely imagination, proof, and dual proof. In a first step, I will present an axiom system and a tableau calculus for a propositional logic of imagination ascriptions. This logic combines a certain modal logic of agency, dstit-logic, with the neighbourhood semantics of non-normal modal logics.In a second step, I will present some thoughts on a formal analysis of the inferential actions of proof and dual proof. Such an analysis requires the consideration of a particular deductive system. The idea is to conceptualize inferring as seeing to it that one has a proof, respectively a dual proof, in the deductive system in question. The resulting modal inference operators can be added to Artemov andNogina's epistemic logic with justification.

- S. Artemov and E. Nogina, Introducing justification into epistemic logic, Journal of Logic and Computation 15, 2005, 1059-1073.
- G. Olkhovikov and H. Wansing, An axiom system and a tableau calculus for STIT imagination logic, 2015, submitted.
- H. Wansing, Falsification, natural deduction, and bi-intuitionistic logic, Journal of Logic and Computation 26, 2016, 425-450, published online July 2013, doi:10.1093/logcom/ext035.
- H. Wansing, Remarks on the logic of imagination. A step towards understanding doxastic control through imagination, Synthese, published online October 2015, doi: 10.1007/s11229-015-0945-4.
- H. Wansing, On split negation, strong negation, information, falsification, and verification, in: K. Bimbó (ed.), J. Michael Dunn on Information Based Logics, Springer, to appear 2016.