Analogical Proportions and Multiple-Valued Logics

National audienceRecently, a propositional logic modeling of analogical proportions, i.e., statements of the form “A is to B as C is to D”, has been proposed, and has then led to introduce new related proportions in a general setting. This framework is well-suited for analogical reasoning and classification tasks about situations described by means of Boolean properties. There is a clear need for extending this approach to deal with the cases where i) properties are gradual ; ii) properties may not apply to some situations ; iii) the truth status of a property is unknown. The paper investigates the appropriate extension in each of these three cases

Supervised Classification Using Homogeneous Logical Proportions for Binary and Nominal Features

International audienceThe notion of homogeneous logical proportions has been recently introduced in close relation with the idea of analogical proportion. The four homogeneous proportions have intuitive meanings, which can be related with classification tasks. In this paper, we proposed a supervised classification algorithm using homogeneous logical proportions and provide results for all. A final comparison with previous works using similar methodologies and with other classifiers is provided

Picking the one that does not fit - A matter of logical proportions

National audienceQuiz or tests about reasoning capabilities often pertain to the perception of similarity and dissimilarity between situations. Thus, one may be asked to complete a series of entities $A$, $B$, $C$ by an appropriate $X$, or to pick the one that does not fit in a list. It has been shown that the first problem can receive a solution by solving analogical proportion equations between the representations of the entities in a logical setting, where we assume that $X$ should be such that $A$ is to $B$ as $C$ is to $X$. In this paper, we focus on the second problem, and we show that it can be properly handled by means of heterogeneous proportions that are the logical dual of the homogeneous proportions involved in the modeling of analogical proportions and related proportions. Thus, the formal setting of logical proportions, to which homogeneous and heterogeneous proportions belong, provides an appropriate framework for handling the two problems in a coherent way. As it already exists for homogeneous proportions, a particular multiple-valued logic extension of heterogeneous proportions is discussed (indeed being an intruder in a group may be a matter of degree)

Homogenous and heterogeneous logical proportions

International audienceCommonsense reasoning often relies on the perception of similarity as well as dis- similarity between objects or situations. Such a perception may be expressed and summarized by means of analogical proportions, i.e., statements of the form “A is to B as C is to D”. Analogy is not a mere question of similarity between two objects (or situations), but rather a matter of proportion or relation between objects. This view dates back to Aristotle and was enforced by Scholastic philosophy. Indeed, an analogical proportion equates a relation between two objects with the relation between two other objects. As such, the analogical proportion “A is to B as C is to D” poses an analogy of proportionality by (implicitly) stating that the way the two objects A and B, otherwise similar, differ is the same way as the two objects C and D, which are similar in some respects, differ

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

From Analogical Proportion to Logical Proportions

International audienceGiven a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( a∧b and a¯∧b¯), or dissimilarity indicators ( a∧b¯ and a¯∧b) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the form “a is to b as c is to d”. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations (a¯,b¯,c¯,d¯)). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions

Dimensions of creative evaluation: Distinct design and reasoning strategies for aesthetic, functional and originality judgments

Our analysis of the DTRS 10 dataset examined evaluative reasoning taking place during expert ‘design critiques’. We focused on key dimensions of creative evaluation (originality, functionality and aesthetics) and ways in which these dimensions impact reasoning strategies and suggestions offered by experts for how the student could continue. Each dimension was associated with a specific underpinning ‘logic’ determining how these dimensions were evaluated in practice. Our analysis clarified how these dimensions triggered reasoning strategies such as running mental simulations or making design suggestions, ranging from ‘go/kill’ decisions to loose recommendations to continue without directional steer. The findings advance our theoretical understanding of evaluation behavior in design and alert practicing design evaluators to the nature and consequences of their critical appraisals