Related papers: Norms on possibilities I: forcing with trees and c…
Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework,…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
In problem-solving, we humans can come up with multiple novel solutions to the same problem. However, reinforcement learning algorithms can only produce a set of monotonous policies that maximize the cumulative reward but lack diversity and…
We define forcing orders which add witnesses to the failure of various forms of Friedman's Property. These posets behave similarly to the forcing order adding a nonreflecting stationary set but have the advantage of allowing the…
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
We study methods to obtain the consistency of forcing axioms, and particularly higher forcing axioms. We first force over a model with a supercompact cardinal $\theta>\kappa$ to get the consistency of the forcing axiom for $\kappa$-strongly…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
Norms with sanctions have been widely employed as a mechanism for controlling and coordinating the behavior of agents without limiting their autonomy. The norms enforced in a multi-agent system can be revised in order to increase the…
We introduce the notion of nonuniform coercion, which is the promotion of a value of one type to an enriched value of a different type via a nonuniform procedure. Nonuniform coercions are a generalization of the (uniform) coercions known in…
We introduce Gowers--Matet forcing with a finite sequence of pairwise non-isomorphic Ramsey ultrafilters over $\omega$, and with this forcing we settle the long-standing problem of the spectrum of numbers near-coherence classes. We prove…
Given an inner model $W \subset V$ and a regular cardinal $\kappa$, we consider two alternatives for adding a subset to $\kappa$ by forcing: the Cohen poset $Add(\kappa,1)$, and the Cohen poset of the inner model $Add(\kappa,1)^W$. The…
In a self-contained way, we deal with revised countable support iterated forcing for the reals. We improve theorems on preservation of the property UP, weaker than semi proper, and we hopefully improve the presentation. We continue [Sh:b,…
We define typical forcings encompassing many informal forcing arguments in bounded arithmetic and give general conditions for such forcings to produce models of the universal variant of relativized $T^1_2$. We apply this result to study the…
Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
First of all we give some reasons that "natural proofs" built not a barrier to prove P $\not=$ NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the…
Farkas' lemma is an ubiquitous tool in optimisation, as it provides necessary and sufficient conditions to have $b \in A(P)$, where $P$ is a closed convex cone, $A$ is a (continuous) linear mapping and $b$ is a fixed vector. The standard…
We view sorites in terms of stimuli acting upon a system and evoking this system's responses. Supervenience of responses on stimuli implies that they either lack tolerance (i.e., they change in every vicinity of some of the stimuli), or…