Trivalent Suspension, Uncertainty and Reasoning with Conditionals

The international workshop on "Trivalent Suspension, Uncertainty and Reasoning with Conditionals" (TSUC) from August 30 - September 1, 2023 aims to bring together renowned researchers from philosophy, logic, formal epistemology, and mathematics to discuss the major issues, contemporary methodologies that have arisen in the study of suspension, uncertainty, and conditionals. We will investigate a specific perspective concerning trivalent logic, probability and conditionals. Specifically, this workshop intends to bring together researchers to introduce and discuss i) major TSUC research issues that have arisen in recent years, ii) innovative methodologies developed in response to such issues, iii) the connections between the three components of TSUC, and iv) major TSUC research challenges in its future development. Such research issues include the formal models of judgment suspension, indeterminism, uncertainty inference, many-valued connectives and consequences, subjective probability, conditional probabilities, trivalent conditionals, branching time structure, and so forth. We will be able to understand the major issues, and research problems and gaps for the future development of TSUC.

The Workshop will start on Wednesday, August 30, at 2 p.m. and finish on Friday, September 1, at 2 p.m.. The venue is the campus of the University of Regensburg (Room H26 of the "Vielberth-Gebäude").

Caitlin Canonica (Ruhr-Universität Bochum, Germany)
John Cantwell (KTH Kungliga Tekniska högskolan, Sweden)
Massimiliano Carrara (Università degli Studi di Padova, Italy)
Mario Günther (Ludwig-Maximilians-Universität München, Germany)
Sven Ove Hansson (KTH Kungliga Tekniska högskolan, Sweden)
Tim Kraft (University of Regensburg, Germany)
Ondrej Majer (Academy of Sciences of the Czech Republic, Czech Republic)
Niki Pfeifer (University of Regensburg, Germany)
Hans Rott (University of Regensburg, Germany)
Giuseppe Sanfilippo (Università degli Studi di Palermo, Italy)
Daniela Schuster (Universität Konstanz, Germany)
Verena Wagner (Universität Konstanz, Germany)
Wei Zhu (University of Regensburg, Germany)

Caitlin Canonica

Reasoning from a Negated Conditional: New Experimental Evidence

John Cantwell

Sequence/Path Semantics for the Suppositional Analysis of the Conditional

Massimiliano Carrara

A Semantic for a Radical Kind of Suspension

It is widely accepted that suspension constitutes a question-directed attitude. In fact, when expressing suspension, we naturally employ interrogative complements rather than declarative ones.
There can be several reasons why a question remains unanswered, leading to the suspension of judgment. One possible reason is that the obtained answer does not pertain to the subject-matter of the question. For instance, consider the statement "Alice suspends judgment whether it rains tomorrow." The suspension occurs not only because the information obtained from the answer is, for example vague - so that one does not have enough information to decide whether the sentence "it will rain tomorrow" is true or false - but primarily because the answer itself is unrelated to the subject-matter of the question, because it pertains, for example, to something like tourism in Pinarella.
In this talk, I explore a Bochvar logic (B), originally designed to address vagueness, belonging to the family of Weak Kleene logics. Recently, J.C. Beall (2016) proposed an interpretation of the truth values of B in terms of true-on-topic, false-on-topic, and out-of-topic. To further advance the understanding of B, I develop a game-theoretic semantics that distinguishes between cases where a discussion is on-topic and those where it is not.
When a discussion goes off-topic, the most appropriate action is to suspend judgment on the sentence under consideration. This type of suspension is radical and differs significantly from a vagueness-driven suspension, which, unlike the former, can be lifted once new evidence is introduced.

References

Beall, J. (2016). Off-topic: A new interpretation of weak-kleene logic. The Australasian Journal of Logic, 13(6):136-142.

Mario Günther

Suspension of Judgment and Causation

In this talk, I present an epistemic analysis of causation. The core of the analysis is the epochetic conditional: an agent believes C » E just in case she can infer E upon supposing C after suspending judgment on both C and E. Given that an agent believes C and E to be distinct actual events, the agent believes C to be a cause of E if and only if the agent believes the epochetic conditional C » E. I show that this analysis accounts well for many causal scenarios in comparison to the counterfactual approach.

Sven Ove Hansson

How to Combine Probabilities and Full Beliefs?

One of the major problems in formal epistemology is the difficulty of combining probabilistic and dichotomous (all-or-nothing) beliefs in one and the same formal framework. Based on the properties of actual human belief systems, a set of ten desiderata is proposed for belief system models that contain both probabilistic and full beliefs. Previously proposed combined belief systems are shown to fall short of these desiderata. A proof of concept is provided to show that they can be satisfied in a formal model. In the proposed model, the amnesia problem of probabilistic updating is solved by introducing infinitesimal probabilities as carriers of memories of beliefs that have been given up. In the resulting system of probability revision, contingent propositions can be transferred in both directions between full beliefs and lower, graded, degrees of belief, in a way that mirrors real-life acquisitions and losses of full beliefs. The subsystem consisting of full beliefs has a pattern of change that constitutes a credible system of dichotomous belief change.

Tim Kraft

Ignorance First Epistemology: Understanding Suspension in Terms of Ignorance

According to knowledge first epistemology (defended prominently by Williamson and others), belief and other epistemic concepts can be defined and explained in terms of knowledge. For example, belief can be defined in terms of knowledge, not the other way around. According to ignorance first epistemology, suspension and other "negative“ counterparts of epistemic concepts can be defined and explained in terms of ignorance. For example, suspension can be defined in terms of ignorance, not the other way around: Suspension is the mental state(s) – whatever it or they are – that is meant to track(s) one's own ignorance. In this talk I introduce this approach to understanding suspension and try to highlight some of the insights into ignorance and suspension it offers.

Ondrej Majer

Reasoning About Uncertainty in Frameworks with Incomplete and Contradictory Information

Actual epistemic subjects sometimes face situations when they have to make a decision in situations when only available information is inconsistent. Consequently systems of epistemic logic that attempt to represent more realistic agents, have to use frameworks which can deal with inconsistent information in a non-trivial way. One such framework is Belnap-Dunn logic (BD), designed for processing inconsistent/incomplete data in databases is (“How a computer should think”).In this paper, we present a probabilistic extension of BD and discuss its properties. We provide methods for conditionalization (equivalents of Bayes’ and Jeffrey updating) and aggregation of information from different possibly contradictory sources. We also show how to define more general measures of uncertainty over BD logic and finally introduce models of reasoning with inconsistent/incomplete uncertain information using the framework of two layer modal logics.

Niki Pfeifer

Suspension: Perspectives from Probability Logic and Experimental Philosophy

Abstract: After characterising coherence-based probability logic as a rationality framework for experimental philosophy, I investigate selected problems of suspension. Specifically, I discuss how suspension can be rationally represented by tools of probability logic, imprecise probabilities, and beliefs in conditionals under uncertainty. Moreover, I discuss pragmatic problems in the experimental philosophical investigations on reasoning about what cannot be known and how such problems can be solved. Finally, I present selected experiments on human reasoning about uncertain conditionals to illustrate the approach from normative and descriptive perspectives.

Hans Rott (joint work with Wei Zhu)

The Dynamics of Non-belief (With Modesty)

Abstract: "Suspension of judgment" is an ambiguous term that may refer either to a doxastic state ("suspended judgment") or to a doxastic action ("suspending judgment"). Based on a simple non-belief account, this paper presents a formal study of both aspects of suspension. We first introduce the notion of a suspension set (a set of non-beliefs) and determine its logical structure. Then we present the classical AGM operations of belief revision and belief contraction and give characterizations of them that refer to suspension sets rather than belief sets. Finally, we study the suspension operation, a symmetric cousin of belief contraction, and characterize it both in terms of belief sets and in terms of suspension sets. Belief contraction and belief suspension thereby get reinterpreted as two different forms of the expansion of suspension sets. The project is interesting because in contrast to belief revision and belief contraction, the suspension operation is symmetric with respect to negation: suspending judgment on A is the same as suspending judgment on ¬A. Most of our results are premised on an assumption of modesty: for every person there is always at least one proposition on which she suspends judgment.

Giuseppe Sanfilippo

A Probabilistic Analysis of Selected Notions of Iterated Conditioning and of a Generalization of the Conjunction of Two Conditional Events

Abstract: It is well know that basic conditionals satisfy some desirable basic logical and probabilistic properties, such as the compound probability theorem, but checking the validity of these becomes trickier when we switch to compound and iterated conditionals. We consider de Finetti’s notion of conditional as a three-valued object and as a conditional random quantity in the betting framework. We recall the notions of conjunction and disjunction among conditionals in selected trivalent logics. We also recall the notions of compound and iterated conditionals in the setting of conditional random quantities. Then, in the framework of specific threevalued logics we analyze the notions of iterated conditioning introduced by Cooper-Calabrese, by de Finetti, by Farrell, and by Cantwell. We show that the compound probability theorem and other basic properties are not preserved by these objects, by also computing some probability propagation rules. Then, for each trivalent logic we introduce an iterated conditional as a suitable random quantity which satisfies the compound prevision theorem and some of the desirable properties. We also check the validity of two generalized versions of Bayes’ Rule for iterated conditionals. We observe that all the basic properties are satisfied only by the iterated conditional which is based on the notion of conjunction of conditionals defined in the setting of conditional random quantities. This conjunction for two conditional events A|H and B|K is defined as a five-valued object with set of possible values 1,0,x,y,z, where x=P(A|H), y=P(B|K), and z is its prevision. We also propose a generalisation of this conjunction where the probability values x and y are replaced by two arbitrary values a and b in [0,1]. Finally, we study the probability propagation rule for this object and we give a probabilistic interpretation in terms of betting scheme.

Daniela Schuster

Suspension and Higher-Order Reasoning in Default Logic

Intelligent, artificial systems make our lives easier in many ways.  In decision-making processes, expert systems often advise us in one direction or another, by following some chain of non-monotonic rules.

One of the main challenges for a system operating on non-monotonic reasoning is to find strategies for solving conflicts that arise due to the defeasibility of the non-monotonic arguments. A system, which is equipped with a defeasible argument for a proposition p and another defeasible argument against p, will end up with a contradiction if both arguments are triggered. In this talk, I will consider the framework of default logic (Horty, 2011) and I will argue that the currently available solutions for conflicted situations are all deficient. The current attempts are more intended to rapidly overcome conflicting situations than to properly deal with the conflict. This is leading to decisions that are made arbitrarily and that are thus not explainable.

I want to propose an alternative solution that consists of an adjustment of default logic that allows the reasoner to represent a conflicting situation via the tool of suspended judgment. I will show, how this adjustment enriches the framework such that different doxastic stances as well as higher-order reasoning can be represented.

Verena Wagner

Commitments and Suspension

In epistemology, suspension of judgment is typically taken to be the third doxastic stance besides belief and disbelief. In this talk, I will challenge the view that there is but one neutral state of mind which can capture all the cases that we would intuitively classify as cases of suspension or neutrality. Yet, if we allow for more than one neutral state of mind, we also need a unifying theory that explains why these different phenomena still fall under the same genus.

I will suggest an analysis of suspending judgment in terms of committing to indecision which allows for different commitments that are reflective of the different kinds of suspension. This is relevant for epistemology because different kinds of commitments also require different standards of rational assessment.

Wei Zhu

Can Many-Valued Logics Contribute New Insights into Belief Suspension?

The term “belief suspension” has been used to refer to a non-belief attitude, to an undetermined epistemic attitude, or to an unsettled epistemic attitude. Many recent discussions in epistemology have tried to understand its nature, its implications, and its rationality requirements. By taking into account the still undetermined nature of belief suspension, one could consider its potential as an epistemic interpretation of a three-valued logic. Alternatively, one can regard suspension as a third doxastic attitude towards a proposition bearing a third truth value. In this case, we could consider the idea of using many-valued logics as a basis for analyzing belief suspension within a belief revision framework. In both cases, understanding the connection between many-valued logics and belief suspension becomes essential. Consequently, in this talk, we will assume the non-belief account of suspension, and we will address the question: Can many-valued logics contribute new insights into belief suspension?