Related papers: Arrow-Sen theory simplified
We study abduction in First Order Horn logic theories where all atoms can be abduced and we are looking for preferred solutions with respect to three objective functions: cardinality minimality, coherence, and weighted abduction. We…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
For many real-world classification problems, e.g., sentiment classification, most existing machine learning methods are biased towards the majority class when the Imbalance Ratio (IR) is high. To address this problem, we propose a set…
In recent years they have been numerous works that aim to automate relational verification. Meanwhile, although Constrained Horn Clauses (CHCs) empower a wide range of verification techniques and tools, they lack the ability to express…
Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual…
The basic one in this work is the axiomatic set theory $NBG$ (von Neumann-Bernays-G{\"o}del), which is a first-order theory with its own axioms, including in particular the axiom of choice ${\bf AC}$ and the axiom of regularity ${\bf RA}$.…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as…
We consider priority-based school choice problems with farsighted students. We show that a singleton set consisting of the matching obtained from the Top Trading Cycles (TTC) mechanism is a farsighted stable set. However, the matching…
One of the basic assumptions underlying Bell's theorem is the causal arrow of time, having to do with temporal order rather than spatial separation. Nonetheless, the physical assumptions regarding causality are seldom studied in this…
Constructing new and more challenging tasksets is a fruitful methodology to analyse and understand few-shot classification methods. Unfortunately, existing approaches to building those tasksets are somewhat unsatisfactory: they either…
We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…
We begin with a context more general than set theory. The basic ingredients are essentially the object and functor primitives of category theory, and the logic is weak, requiring neither the Law of Excluded Middle nor quantification. Inside…
Latent reasoning offers a computation-efficient alternative to Chain-of-Thought but often suffers from performance degradation due to distributional misalignment and ambiguous chain definitions. Ideally, latent reasoning should function as…
Text simplification (TS) aims to reduce the lexical and structural complexity of a text, while still retaining the semantic meaning. Current automatic TS techniques are limited to either lexical-level applications or manually defining a…
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we may use a program abstraction in which transitions are described by monotonicity constraints over…
This work proposes a novel adaptation of a pretrained sequence-to-sequence model to the task of document ranking. Our approach is fundamentally different from a commonly-adopted classification-based formulation of ranking, based on…
We provide a graphical treatment of SAT and #SAT on equal footing. Instances of #SAT can be represented as tensor networks in a standard way. These tensor networks are interpreted by diagrams of the ZH-calculus: a system to reason about…
*Minimal sufficient reasons* represent a prevalent form of explanation - the smallest subset of input features which, when held constant at their corresponding values, ensure that the prediction remains unchanged. Previous *post-hoc*…
Gibbard and Satterthwaite have shown that the only single-valued social choice functions (SCFs) that satisfy non-imposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…