You are here
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
At least three distinct definitions of logical consequence have been proposed in many-valued logic, which coincide in the two-valued case, but come apart as soon as three truth values come into play. Those definitions include so-called 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).
While obvious conceptual and logical links exist between those definitions, the question of whether those schemes can be subsumed under a common and more abstract template is not as obvious as it might seem. In this paper, we examine whether those definitions together carve out a natural class of consequence relations. We respond positively by identifying three minimal constraints all such schemes satisfy, namely: truth-functionality, bivalence-compliance, and a constraint of value-monotonicity. We call 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.
Finally, we discuss the significance of our result for the problem of characterizing what counts as a 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.
(Joint work with Emmanuel Chemla, and Benjamin Spector)
Wiebe van der Hoek (University of Liverpool)
Program models and semi-public environments
We develop a logic for reasoning about "semi-public environments", that is, environments in which a process is executing, and where agents in the environment have partial and potentially different views of the process. Previous work on this problem illustrated that it was problematic to obtain both an adequate semantic model and a language for reasoning about semi-public environments. We here use "program models" for representing the changes that occur during the execution of a program. These models serve both as syntactic objects and as semantic models, and are a modification of action models in Dynamic Epistemic Logic, in the sense that they allow for ontic change (i.e., change in the world or state). We show how program models can elegantly capture a notion of observation of the environment. The use of these models resolves several difficulties identified in earlier work, and admit a much simpler treatment than was possible in previous work on semi-public environments.
(Joint work with Davide Grossi, Christos Moyzes, and Michael Wooldridge)
Benjamin Icard (IJN - ENS)
The ‘Surprise Deception Paradox’: a conceptual and logical insight into veridical deception
Epistemologists have devoted efforts to the analysis of 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].
In this talk, I will focus on one aspect of veridical deception which, as far as I know, has not been so far examined in the literature: the ability for someone to deceive while telling the truth about their deceitful attitude, that is to say the capacity for them to deceive after having 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.
In a nutshell, even if the deceiver’s announcement is 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
Sentences involving plural predication are sometimes neither true nor false. An example of this is (1) in a situation where Mr. Benfleet published exactly half of the books in question. (1) Mr. Benfleet published/didn't publish the books. Building on work by Link 1983 and Lepage 1992, I present an algebraic semantics for a logic with generalised quantifiers that is designed to capture the following features of natural language: (i) The pattern of trivalence of both distributive and collective predicates of pluralities. (ii) The existence of quantification over pluralities. (iii) The interaction of quantifiers (over both atoms and pluralities) with the kind of trivalence that arises from plural predication.
It turns out that the same algebraically formulated constraint, when generalised over domains, can account for all of these features: When applied to predicates, it yields a pattern of undefinedness, and when applied to quantifiers (as predicates of predicates), it captures the interaction of quantifiers with this kind of trivalence.
Ekaterina Kubyshkina (IHPST - Paris 1)
Representing ignorance: a truth-functional approach
We present some ongoing work about the duality between the notions of knowledge and ignorance. In particular, we argue that these notions are not necessarily inter-definable. In order to defend this idea, we provide the logical tools to characterize ignorance independently of knowledge.
Traditionally, the notion of knowledge is represented in epistemic logic by the K-operator. The possible worlds semantics for this operator was provided by Hintikka (1962). In such a semantics the notion of ignorance is defined via the K-operator. An alternative characterization of this notion can be found in “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.
Along these lines we introduce a four-valued logic (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.
References
- 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.