Related papers: DRAT and Propagation Redundancy Proofs Without New…
We introduce an information-theoretic framework for caching in derivation-based reasoning engines under independent premise erasure. Two decoder models are compared: a coded scheme using an arbitrary bit-string cache with a general-purpose…
This paper introduces a uniform substitution calculus for differential refinement logic dRL. The logic dRL extends the differential dynamic logic dL such that one can simultaneously reason about properties of and relations between hybrid…
Decision trees (DTs) epitomize the ideal of interpretability of machine learning (ML) models. The interpretability of decision trees motivates explainability approaches by so-called intrinsic interpretability, and it is at the core of…
Sparse representation over redundant dictionaries constitutes a good model for many classes of signals (e.g., patches of natural images, segments of speech signals, etc.). However, despite its popularity, very little is known about the…
We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In particular, using the notions commutativity and semi-commutativity, we show how the well-known…
Discourse Representation Structure (DRS) is an innovative semantic representation designed to capture the meaning of texts with arbitrary lengths across languages. The semantic representation parsing is essential for achieving natural…
A {\it dynamic reasoning system} (DRS) is an adaptation of a conventional formal logical system that explicitly portrays reasoning as a temporal activity, with each extralogical input to the system and each inference rule application being…
We study here the well-known propagation rules for Boolean constraints. First we propose a simple notion of completeness for sets of such rules and establish a completeness result. Then we show an equivalence in an appropriate sense between…
Array structures based on the sum and difference co-arrays provide more degrees of freedom (DOF). However, since the growth of DOF is limited by a single case of sum and difference co-arrays, the paper aims to design a sparse linear array…
Duality is a foundational tool in robust and distributionally robust optimization (RO and DRO), underpinning both analytical insights and tractable reformulations. The prevailing approaches in the literature primarily rely on saddle-point…
This paper studies propositional proof systems in which lines are sequents of decision trees or branching programs - deterministic and nondeterministic. The systems LDT and LNDT are propositional proof systems in which lines represent…
Given a constraint satisfaction problem (CSP) predicate $P \subseteq D^r$, the non-redundancy (NRD) of $P$ is maximum-sized instance on $n$ variables such that for every clause of the instance, there is an assignment which satisfies all but…
In this paper, we propose a structured Robust Adaptive Dic-tionary Pair Learning (RA-DPL) framework for the discrim-inative sparse representation learning. To achieve powerful representation ability of the available samples, the setting of…
Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…
Shannon's rate-distortion theory treats source symbols as unstructured labels. When the source is a knowledge base equipped with a logical proof system, a natural fidelity criterion is closure fidelity: a reconstruction is acceptable if it…
We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
We use the English model of BERT and explore how a deletion of one word in a sentence changes representations of other words. Our hypothesis is that removing a reducible word (e.g. an adjective) does not affect the representation of other…
We present a distributionally robust optimization (DRO) approach for the transmission expansion planning problem, considering both long- and short-term uncertainties on the system demand and non-dispatchable renewable generation. On the…
Explainability is a key component in many applications involving deep neural networks (DNNs). However, current explanation methods for DNNs commonly leave it to the human observer to distinguish relevant explanations from spurious noise.…