Related papers: The logic behind desirable sets of things, and its…

Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…

A description of the environment cognition process by intelligent systems with a fixed set of system goals is suggested. Such a system is represented by the set of its goals only without any models of the system elements or the environment.…

Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between…

We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant…

We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…

Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…

Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…

It is conventional wisdom in machine learning and data mining that logical models such as rule sets are more interpretable than other models, and that among such rule-based models, simpler models are more interpretable than more complex…

Robotic systems for household object rearrangement often rely on latent preference models inferred from human demonstrations. While effective at prediction, these models offer limited insight into the interpretable factors that guide human…

Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…

Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…

Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…

This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…

Many online shops offer functionality that help their customers navigate the available alternatives. For instance, options to filter and to sort goods are wide-spread. In this paper we show that sorting and filtering can be used by rational…

Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…

Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…