Related papers: Nonmonotonic inference operations
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
As far as algebraic properties are concerned, the usual addition on the class of ordinal numbers is not really well behaved; for example, it is not commutative, nor left cancellative etc. In a few cases, the natural Hessemberg sum is a…
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…
Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…
Infinite order linear recurrences are studied via kneading matrices and kneading determinants. The concepts of kneading matrix and kneading determinant of an infinite order linear recurrence, introduced in this work, are defined in a purely…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
We provide estimates for the convolution product of an arbitrary number of "resurgent functions", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under…
We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability constraints and on a preferred-model…
Kantorovich operators are non-linear extensions of Markov operators and are omnipresent in several branches of mathematical analysis. The asymptotic behaviour of their iterates plays an important role even in classical ergodic, potential…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.
We investigate several technical and conceptual questions. Our main subject is the investigation of independence as a ternary relation in the context of non-monotonic logic. In the context of probability, this investigation was started by…
Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and…
We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…
A number of writers(Joseph Halpern and Fahiem Bacchus among them) have offered semantics for formal languages in which inferences concerning probabilities can be made. Our concern is different. This paper provides a formalization of…
In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, exhibiting a classical…