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We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path…
Digraphs provide an alternative syntax for propositional logic, with digraph kernels corresponding to classical models. Semikernels generalize kernels and we identify a subset of well-behaved semikernels that provides nontrivial models for…
The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…
Code generation has shown great promise in assisting software development. A fundamental yet underexplored question is how the choice of code representation affects model performance. While existing studies employ various representations,…
DNA-based storage is an emerging technology that enables digital information to be archived in DNA molecules. This method enjoys major advantages over magnetic and optical storage solutions such as exceptional information density, enhanced…
Graph neural networks (GNNs) are the predominant approach for graph-based machine learning. While neural networks have shown great performance at learning useful representations, they are often criticized for their limited high-level…
This paper describes a novel approach to synthesize molecular reactions to train a perceptron, i.e., a single-layered neural network, with sigmoidal activation function. The approach is based on fractional coding where a variable is…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
We propose a new interpretability method for neural networks, which is based on a novel mathematico-philosophical theory of reasons. Our method computes a vector for each neuron, called its reasons vector. We then can compute how strongly…
Traditional automated theorem provers have relied on manually tuned heuristics to guide how they perform proof search. Recently, however, there has been a surge of interest in the design of learning mechanisms that can be integrated into…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Explaining why an answer is in the result of a query or why it is missing from the result is important for many applications including auditing, debugging data and queries, and answering hypothetical questions about data. Both types of…
Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
DNA computation could in principle solve the satisfiability (SAT) problem due to the operations in parallel on extremely large numbers of strands. We demonstrate some quantum gates corresponding to the DNA ones, based on which an…
Over the last few years, machine learning over graph structures has manifested a significant enhancement in text mining applications such as event detection, opinion mining, and news recommendation. One of the primary challenges in this…
Provenance is an increasing concern due to the ongoing revolution in sharing and processing scientific data on the Web and in other computer systems. It is proposed that many computer systems will need to become provenance-aware in order to…