Conditionals 2026

Title: Situated Conditionals

Abstract: Conditionals are useful for modelling many forms of everyday human reasoning but are not always sufficiently expressive to represent the information we want to reason about. In this paper, we make a case for a form of situated conditional. By situated, we mean that there is a context, based on an agent’s beliefs and expectations, that works as background information in evaluating a conditional, and we allow such a context to vary. These conditionals are able to distinguish, for example, between expectations and counterfactuals. Formally, they are shown to generalise the conditional setting in the style of Kraus, Lehmann, and Magidor. We show that situated conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postu- lates. With the semantics in place, we define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks.

Title: Metainference arrows in radically substructural logics

Abstract: Gentzen's calculus LK makes a sharp distinction between operational and structural rules. The term ''substructural logics'' refers to logics where some structural rule is restricted. The traditional study of substructurality focused on the rules of Contraction, Weakening, or Exchange. However, over the past fifteen years ''radical substructurality'' ---restrictions of cut or identity--- has gained significant attention within the philosophical logic community. This talk provides an overview of the motivation, developments, challenges and open questions about the consequence arrow in the context of radically substructural logics.

Title: Coherent reasoning with conditionals

Abstract: Suppose Berta and Beto were planning to go to Barcelona last weekend. How justified is it to infer ''they travelled by train'' on the basis that ''If they went to Barcelona, then they travelled by train'' and ''they went to Barcelona''? To answer this question, we need to assess how the statements that make up this inference are related to one another, and what the individual statements mean. The most contested and arguably difficult to establish meaning among the statements above is that of the conditional. Theories of the meaning(s) of conditionals are difficult to test empirically because they are often specified only at the verbal level, and make overlapping predictions. To address these limitations, we use coherence-based probability logic to formalise seven accounts of the semantics of conditionals (plus a ''guessing'' account), along with the predictions of each account for people's responses to eight inference forms. We then integrate the results of this formal analysis into a hierarchical Bayesian mixture model. The model includes a parameter to estimate the probability that responses in a given experiment trial are caused by inattentiveness or guessing rather than by any particular interpretation of conditionals, and that people can differ in the account(s) they use to inform their responses across trials. We illustrate through simulations how this Bayesian model makes it possible to test empirical predictions of competing accounts of conditionals, even when they differ in complexity and make overlapping predictions.

Title: Playing with Spheres, Preorders, and Rankings.

Abstract: In this presentation, we will discuss the ''system of spheres'' as a conceptual framework for generating ideas in belief change. We will begin by introducing the AGM theory using the Spheres System, followed by examples of withdrawal functions such as Severe, Systematic, and Ring. Subsequently, we will explore non-prioritized belief change methods, including Selective and Credibility-Limited Revision. The third segment will focus on iteration, the DP postulates, and examples such as improvement, revision by comparison, and bounded revision. Finally, we will demonstrate how to define models that emphasize special spheres, using examples like Credibility-Limited Revision, abductive belief change, and prototype revision.

Title: Constructive conditionals: a proof-theoretic view

Abstract: Conditional logics, introduced by David Lewis in 1973, extend classical propositional logic with a binary modal connective - the conditional - suitable for representing fine-grained notions of conditionality.

Constructive and intuitionistic counterparts of conditional logics have recently been studied by Weiss, Ciardelli and Liu, and Olkhovikov. Based on selection-function semantics and developed in analogy with intuitionistic modal logic, these systems incorporate forms of constructive reasoning into the conditional framework. A key difference from their classical counterparts is that the would-conditional and the might-conditional are no longer interdefinable.

In this talk, we use proof-theoretic methods to investigate the landscape of constructive and intuitionistic conditional logics. First, we introduce sequent calculi for the constructive conditional logics with a would-conditional only, studied by Weiss and Ciardelli and Liu. Using proof-theoretic intuitions, we then extend these logics with a might-conditional. Finally, we present nested-style sequent calculi for the stronger intuitionistic conditional logic introduced by Olkhovikov. 

This talk is based on https://dl.acm.org/doi/10.1007/978-3-032-06085-3$_-$19, joint work with Tiziano Dalmonte

Title: Galois Connections, Fixpoints and Selections: Towards a Common Framework for Reasoning and Change  

Abstract: This talk presents a general framework for studying selected areas of knowledge representation and reasoning, based on an extension of Formal Concept Analysis. Starting from the correspondence between theories and models induced by a logical satisfaction relation, we use Galois connections and fixpoints to obtain dual syntactic and semantic perspectives on knowledge. Building on this structure, we study transformations on both sides, connecting non-monotonic and belief change operators on the syntactic side with selection functions on the semantic side. This provides a common perspective on belief change theory and non-monotonic logics, while drawing on ideas from decision theory and social choice theory. We further discuss extensions to belief bases and iterated change, as well as applications to model and ontology repair.

Title: Safely Decomposing Conditional Belief Bases Into c-LEG Networks

Abstract: Like Pearl's System Z, c-representations provide a constructive approach to compute a ranking function from a conditional belief base from which further (conditional) beliefs can be derived, meeting major quality standards of nonmonotonic reasoning. This talk proposes a network-based structure for c-representations that allows for cutting down the complexity of reasoning significantly by decomposing the conditional belief base over a hypertree. We introduce c-LEG networks capturing the interactions among conditionals on a syntactical basis in full compatibility with the semantics of c-representations. This allows for reasoning in much smaller local contexts while still complying with the global information provided by the full conditional belief base.

Moreover, we generalize the so-called safety property, which was recently presented in the context of conditional syntax splitting, to ensure that local c-representations of subbases over the hyperedges can be merged to yield global c-representations of the full conditional belief base. This allows for computing global c-representations step by step in local contexts, following the structure of the hypertree.

This talk highlights the role of conditionals as a mediator between human cognition and computational reasoning.   Relevant links can be easily and properly expressed by conditionals that induce a graphical structure which allows for more efficient knowledge representation.

(Joint work with Alexander Hahn, Lars-Phillip Spiegel, Marco Wilhelm, Christoph Beierle, presented and published at KR 2026)

Title: Relevant conditionals vs. relevant conditional probability

Abstract: Relevant logic (see [7], [8]) is undoubtedly the most successful response to the problem of the paradoxes of material implication---patterns of reasoning that are valid according to classical logic, but intuitively invalid. As a consequence of relevance, the classical principles Tertium non datum and Ex falso quodlibet are not valid in relevant frameworks, which makes them suitable for working with incomplete and/or inconsistent information [1], [2].

There have been several proposals in the literature to introduce probability over Belnap-Dunn logic (an implication-free core of relevant logic) ---e.g. [3], [5], [6]. Considerably less attention has been paid to extending probability to relevant implication in order to obtain a probabilistic version of full relevant logic.

The main aim of this paper is to discuss how the concept of relevance transfers to conditional probability---the natural counterpart of conditionals in uncertainty calculi. We explore various possibilities for introducing the probability of a relevant conditional, and we evaluate the motivations and properties of the proposed definitions, paying particular attention to the problem of conditional probability versus the probability of a conditional.

[1] Belnap, N. D. (2019). How a computer should think. In H. Omori \& H. Wansing (Eds.), New essays on Belnap-Dunn logic (Synthese Library, Vol. 418, pp. 35--53). Springer, Cham.

[2] Dunn, J. M. (2010). Contradictory information: Too much of a good thing. Journal of Philosophical Logic, 39, 425--452.

[3] Klein, D., Majer, O., \& Rafiee Rad, S. (2021). Probabilities with gaps and gluts. Journal of Philosophical Logic, 50(5), 1107--1141.

[5] Mares, E. D. (1997). Paraconsistent probability theory and paraconsistent Bayesianism. Logique et Analyse, 375--384.

[6] Mares, E. D. (2004). Relevant logic: A philosophical interpretation. Cambridge University Press. 

[7] Read, S. (1988). Relevant logic. Blackwell.

[8] Restall, G. (2002). An introduction to substructural logics. Routledge.

Title: Conditionals and Non-Monotonicity

Abstract: In the Knowledge Representation (KR) community, conditionals play an important role in describing non-monotonic reasoning formalisms. In such a context, conditionals can be used on the meta-level, as non-monotonic consequence relations, as well as on the object-level, where conditionals are used as non-monotonic connectives that enrich the object language under consideration. In this talk I will discuss both of these ways in which conditionals can be used, as well as their interaction. The talk will be rounded off with a discussion on links between such formalisms developed in the KR community and related work done in Cognitive Science. 

Title: A vector approach to Improvement Operators

Abstract: In this talk we work with the epistemic space of real rankings, a direct extension of rational rankings. We  introduce vector representations for rankings, formulas and for some improvement operators defined in the space of real rankings. These representations are useful to study and understand better some classes of improvement operators. One of our main results is the characterization of ranking-independent and formula independent operators. Finally, as a corollary, we obtain a characterization of the class of translation operators as the intersection of both aforementioned classes.

Title: Uncertainty of Conditionals vs. Conditional Uncertainty

Abstract: This talk presents recent results on the logical connections between uncertainty assigned to a conditional, “if A, then B” (in the Lewis–Stalnaker tradition), and uncertainty assigned to B under the assumption that A holds. Conditional probability provides the paradigmatic model of the latter. The central question is whether, and under what conditions, conditional uncertainty can be represented as uncertainty about the truth of a conditional. Drawing on Lewis’s triviality result, I show that, in the probabilistic setting, this intuitively appealing identification is possible only under restrictive conditions. I then extend the discussion to a recent measure of conditional assertability proposed in the inferentialist literature (Crupi&Iacona, 2020), showing that it, too, cannot generally be identified with uncertainty about a conditional’s truth. I conclude by outlining further directions for this research program and considering the (un)tenability of some intuitive principles concerning the relations among truth, assertability, and the uncertainty assigned to conditionals. 

(based on j.ws.w. T. Flaminio, L. Godo, L. Subirana)

Title: Compound Conditionals, Probabilistic Weak Deduction Theorems, and a General Import-Export Principle

Abstract: This talk concerns conditional events and compound and iterated conditionals within the coherence-based framework of conditional random quantities. We first recall some results on compound conditionals and compare this framework with classical trivalent approaches to conditionals, highlighting the failure of some standard logical and probabilistic properties in those approaches. After recalling the notions of p-consistency and p-entailment, we explain why the classical full deduction theorem fails under p-entailment.

We then present a Probabilistic Weak Deduction Theorem, together with some variants and consequences. Its applications are illustrated by examples involving the failure of transitivity, contraposition, combining evidence, and monotonicity, and by the corresponding weak inference rules obtained after adding suitable premises. 

We next examine the implications of these results for iterated conditionals and the Import--Export principle. The or-to-if inference from A or B to if not-A, then B provides a simple illustration of the failure of both the full deduction theorem and the standard Import--Export principle.

We introduce a General Import--Export principle in which the antecedent may be a conjunction of conditional events. We relate this principle, which does not hold in general, to p-consistency and p-entailment and show that it is satisfied by the Cautious Monotonicity, Cut, and Or rules of System P, even when the hypotheses of the Probabilistic Weak Deduction Theorem are not satisfied. We conclude with a brief comparison with related work and a discussion

of possible further developments.

(This talk is mainly based on the following work:

A.~Gilio, D.~E. Over, N.~Pfeifer, and G.~Sanfilippo, ``On trivalent logics, probabilistic weak deduction theorems,

and a general import-export principle,'' Artificial Intelligence, vol.~337, 2024, Article~104229.)

Title: Challenges for Theory Change and its Conditional Perspective

Abstract: In this talk, I will post three open challenges for theory change, discuss them and its progress on that and the respective connection to conditionals. The first challenge is to understand theory change in broader settings. Typical natural results of theory change do not carry over to general settings, which challenges the conditional perspective on theory change. The next challenges is the extension of iterated change beyond the concepts of Darwiche and Pearl. A natural way of dealing with this is by considering iterated conditionals, but will argue against this approach and post a more pluralistic approach. The third challenges, is regarding understand the link of computational complexity and iterated change. Investigations on complexity of conditional logics could help to clarify the landscape.

9:00 - 9:30 Registration and Opening

9:30 - 10:30 Eduardo Fermé

10:30 - 11:00 Coffee Break

11:00 - 12:00 Ramón Pino Pérez

12:00 - 12:10 Short Break

12:10 - 13:10 Tommie Meyer

13:10 - 15:00 Lunch Break

15:00 - 16:00 Giovanni Casini

16:00 - 16:30 Coffee Break

16:30 - 17:30 Daniel Grimaldi

9:00 - 10:00 Gabriele Kern-Isberner

10:00 - 10:30 Coffee Break

10:30 - 11:30 Nicole Cruz

11:30 - 11:45 Short Break

11:45 - 12:45 Ondrej Majer

12:45 - 15:00 Lunch Break

15:00 - 16:00 Giuseppe Sanfilippo

16:00 - 16:30 Coffee Break

16:30 - 17:30 Giuliano Rosella

9:00 - 10:00 Marianna Girlando

10:00 - 10:30 Coffee Break

10:30 - 11:30 Pablo Cobreros

11:30 - 11:45 Short Break

11:45 - 12:45 Kai Sauerwald

12:45 - 15:00 Lunch Break