Related papers: Topological Forcing Semantics with Settling
Let I be a sigma-ideal sigma-generated by a projective collection of closed sets. The forcing with I-positive Borel sets is proper and adds a single real r of an almost minimal degree: if s is a real in V[r] then s is Cohen generic over V…
This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea…
I introduce a new family of axioms extending ZFC set theory, the $\Sigma_n$-correct forcing axioms. These assert roughly that whenever a forcing name $\dot{a}$ can be forced by a poset in some forcing class $\Gamma$ to have some $\Sigma_n$…
Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We…
We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…
The ground states of topological orders condense extended objects and support topological excitations. This nontrivial property leads to nonzero topological entanglement entropy $S_{topo}$ for conventional topological orders. Fracton…
A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…
We present a new way to control the unfolding of definitions in dependent type theory. Traditionally, proof assistants require users to fix whether each definition will or will not be unfolded in the remainder of a development; unfolding…
We describe the development of a logic for reasoning about specifications in the Edinburgh Logical Framework (LF). In this logic, typing judgments in LF serve as atomic formulas, and quantification is permitted over contexts and terms that…
Token representations in high-dimensional latent spaces often exhibit redundancy, limiting computational efficiency and reducing structural coherence across model layers. Hierarchical latent space folding introduces a structured…
Machine learning tools often rely on embedding text as vectors of real numbers. In this paper, we study how the semantic structure of language is encoded in the algebraic structure of such embeddings. Specifically, we look at a notion of…
We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…
The problem with existing camera-based Deep Reinforcement Learning approaches is twofold: they rarely integrate high-level scene context into the feature representation, and they rely on rigid, fixed reward functions. To address these…
We present a detailed general framework to describe the forcing $\tilde{\mathbb{E}}$, defined by Kellner, Shelah and Tan\u{a}sie to prove the consistency with ZFC of an alternative order of Cicho\'n's maximum. Our presentation is close to…
Capturing semantic relations between sentences, such as entailment, is a long-standing challenge for computational semantics. Logic-based models analyse entailment in terms of possible worlds (interpretations, or situations) where a premise…
In this paper we consider the problem of building rich categories of setoids, in standard intensional Martin-L\"of type theory (MLTT), and in particular how to handle the problem of equality on objects in this context. Any…
Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…
It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
In the field of knowledge representation, the considered epistemic states are often based on propositional interpretations, also called worlds. E.g., epistemic states of agents can be modelled by ranking functions or total preorders on…