Related papers: Theorem Proving Based on Semantics of DNA Strand G…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications. These justifications are expressed in terms of causal graphs…
In this paper, we propose the Neural Knowledge DNA, a framework that tailors the ideas underlying the success of neural networks to the scope of knowledge representation. Knowledge representation is a fundamental field that dedicate to…
The phase diagram of a water solution of DNA and oppositely charged spherical macroions is studied. DNA winds around spheres to form beads-on-a-string complexes resembling the chromatin 10 nm fiber. At small enough concentration of spheres…
Linear logic and the linear {\lambda}-calculus have a long standing tradition in the study of natural language form and meaning. Among the proof calculi of linear logic, proof nets are of particular interest, offering an attractive…
Graph-based interactive theorem provers offer a visual representation of proofs, explicitly representing the dependencies and inferences between each of the proof steps in a graph or hypergraph format. The number and complexity of these…
The idea of computing with DNA was given by Tom Head in 1987, however in 1994 in a seminal paper, the actual successful experiment for DNA computing was performed by Adleman. The heart of the DNA computing is the DNA hybridization, however,…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
Evolution consists of distinct stages: cosmological, biological, linguistic. Since biology verges on natural sciences and linguistics, we expect that it shares structures and features from both forms of knowledge. Indeed, in DNA we…
Every existing knowledge system separates storage from computation. We show this separation is unnecessary and eliminate it. In a standard triple is_a(Apple, Company), domain context lives in the query or the programmer's mind. In a CDC…
In Machine-Assisted Theorem Proving, a theorem proving agent searches for a sequence of expressions and tactics that can prove a conjecture in a proof assistant. In this work, we introduce several novel concepts and capabilities to address…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…
The neural network has become an integral part of modern software systems. However, they still suffer from various problems, in particular, vulnerability to adversarial attacks. In this work, we present a novel program reasoning framework…
Neural networks (NNs) are pervasive across various domains but often lack interpretability. To address the growing need for explanations, logic-based approaches have been proposed to explain predictions made by NNs, offering correctness…
DNA strand displacement systems have proven themselves to be fertile substrates for the design of programmable molecular machinery and circuitry. Domain-level reaction enumerators provide the foundations for molecular programming languages…
The DNA cryptography is a new and very promising direction in cryptography research. DNA can be used in cryptography for storing and transmitting the information, as well as for computation. Although in its primitive stage, DNA cryptography…
In modern age, the increasing complexity of computation and communication technology is leading us towards the necessity of new paradigm. As a result, unconventional approach like DNA coding theory is gaining considerable attention. The…
Ontological commitment, i.e., used concepts, relations, and assumptions, are a corner stone of qualitative reasoning (QR) models. The state-of-the-art for processing raw inputs, though, are deep neural networks (DNNs), nowadays often based…
This paper presents sandra, a neuro-symbolic reasoner combining vectorial representations with deductive reasoning. Sandra builds a vector space constrained by an ontology and performs reasoning over it. The geometric nature of the reasoner…