Analogical reasoning is a powerful inductive mechanism, widely used in human cognition and increasingly applied in artificial intelligence. Formal frameworks for analogical inference have been developed for Boolean domains, where inference is provably sound for affine functions and approximately correct for functions close to affine. These results have informed the design of analogy-based classifiers. However, they do not extend to regression tasks or continuous domains. In this paper, we revisit analogical inference from a foundational perspective. We first present a counterexample showing that existing generalization bounds fail even in the Boolean setting. We then introduce a unified framework for analogical reasoning in real-valued domains based on parameterized analogies defined via generalized means. This model subsumes both Boolean classification and regression, and supports analogical inference over continuous functions. We characterize the class of analogy-preserving functions in this setting and derive both worst-case and average-case error bounds under smoothness assumptions. Our results offer a general theory of analogical inference across discrete and continuous domains.

Even if much has been written about ingredients that trigger laughter, researchers are still far from having completely understood their interplay in the cognitive process that leads a listener to guffaw at a pun or a joke. They are even farther from a detailed analysis and modeling of the mechanisms that are at work in this process. However, in recent articles Dupin de Saint-Cyr and Prade (2020, 2022) took a first step in this direction by laying bare that a belief revision mechanism was solicited in the reception of a narrative joke. Namely the punchline, which triggers a revision, is both surprising and explains perfectly what was reported in the beginning of the joke. A similar idea has been more informally proposed in Ritchie (2002). It is quite clear that this is insufficient for characterizing a narrative joke.

Analogical proportions (AP) are statements of the form "a is to b ascis to d". They compare the pairs of items(a,b) and(c, d) in terms of their differences and similarities. The explicit use of APs in analogical reasoning has contributed to a renewal of its applications, leading to many developments, especially in the last decade; see [30] for a survey. However, even if much has been already done both at the theoretical and at the practical levels, the very nature of APs may not yet be fully understood and their full potential explored. In the following, we survey recent works on APs along three directions: their role in classification tasks [4]; their use for providing explanations [20]; their relation with multi-valued dependencies [21]. This just intends to be an introductory paper, and the reader is referred to the above references for more details on each issue.

Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking function that predicts a linear order of any new set of objects. In this paper, we propose a new approach to object ranking based on principles of analogical reasoning. More specifically, our inference pattern is formalized in terms of so-called analogical proportions and can be summarized as follows: Given objects A,B,C,D, if object A is known to be preferred to B, and C relates to D as A relates to B, then C is (supposedly) preferred to D. Our method applies this pattern as a main building block and combines it with ideas and techniques from instance-based learning and rank aggregation. Based on first experimental results for data sets from various domains (sports, education, tourism, etc.), we conclude that our approach is highly competitive. It appears to be specifically interesting in situations in which the objects are coming from different subdomains, and which hence require a kind of knowledge transfer.

Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking function that predicts a linear order of any new set of objects. In this paper, we propose a new approach to object ranking based on principles of analogical reasoning. More specifically, our inference pattern is formalized in terms of so-called analogical proportions and can be summarized as follows: Given objects $A,B,C,D$, if object $A$ is known to be preferred to $B$, and $C$ relates to $D$ as $A$ relates to $B$, then $C$ is (supposedly) preferred to $D$. Our method applies this pattern as a main building block and combines it with ideas and techniques from instance-based learning and rank aggregation. Based on first experimental results for data sets from various domains (sports, education, tourism, etc.), we conclude that our approach is highly competitive. It appears to be specifically interesting in situations in which the objects are coming from different subdomains, and which hence require a kind of knowledge transfer.

The square of opposition is a structure involving two involutive negations and relating quantified statements, invented in Aristotle time. Rediscovered in the second half of the XXth century, and advocated as being of interest for understanding conceptual structures and solving problems in paraconsistent logics, the square of opposition has been recently completed into a cube, which corresponds to the introduction of a third negation. Such a cube can be encountered in very different knowledge representation formalisms, such as modal logic, possibility theory in its all-or-nothing version, formal concept analysis, rough set theory and abstract argumentation. After restating these results in a unified perspective, the paper proposes a graded extension of the cube and shows that several qualitative, as well as quantitative formalisms, such as Sugeno integrals used in multiple criteria aggregation and qualitative decision theory, or yet belief functions and Choquet integrals, are amenable to transformations that form graded cubes of opposition. This discovery leads to a new perspective on many knowledge representation formalisms, laying bare their underlying common features. The cube of opposition exhibits fruitful parallelisms between different formalisms, which leads to highlight some missing components present in one formalism and currently absent from another.

Boolean games are a game-theoretic framework in which propositional logic is used to describe agents’ goals. In this paper we investigate how agents in Boolean games can reach an efficient and fair outcome through a simple negotiation protocol. We are particularly interested in settings where agents only have incomplete knowledge about the preferences of others. After explaining how generalized possibilistic logic can be used to compactly encode such knowledge, we analyze how a lack of knowledge affects the agreement outcome. In particular, we show how knowledgeable agents can obtain a more desirable outcome than others.

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzzy sets of interpretations, each fuzzy set representing a possibility distribution describing what is known about the state of the world. A possibilistic knowledge base is then viewed as a set of possibility distributions that satisfy it. The refutation method of automated deduction in possibilistic logic, based on previously introduced generalized resolution principle is proved to be sound and complete with respect to the proposed semantics, including the case of partial inconsistency.

The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and generality of probability models, such justifications are often unconvincing. The present paper explores another rationale for probability models. ?Qualitative probability,' which is known to provide stringent constraints on belief representation schemes, is derived from five simple assumptions about relationships among beliefs. While counterparts of familiar rationality concepts such as transitivity, dominance, and consistency are used, the betting context is avoided. The gap between qualitative probability and probability proper can be bridged by any of several additional assumptions. The discussion here relies on results common in the recent AI literature, introducing a sixth simple assumption. The narrative emphasizes models based on unique complete orderings, but the rationale extends easily to motivate set-valued representations of partial orderings as well.

This paper investigates the problem of finding a preference relation on a set of acts from the knowledge of an ordering on events (subsets of states of the world) describing the decision-maker (DM)s uncertainty and an ordering of consequences of acts, describing the DMs preferences. However, contrary to classical approaches to decision theory, we try to do it without resorting to any numerical representation of utility nor uncertainty, and without even using any qualitative scale on which both uncertainty and preference could be mapped. It is shown that although many axioms of Savage theory can be preserved and despite the intuitive appeal of the method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty, but leads to the kind of uncertainty theory encountered in non-monotonic reasoning (especially preferential and rational inference), closely related to possibility theory. Moreover the method turns out to be either very little decisive or to lead to very risky decisions, although its basic principles look sound. This paper raises the question of the very possibility of purely symbolic approaches to Savage-like decision-making under uncertainty and obtains preliminary negative results.