Related papers: Translating SUMO-K to Higher-Order Set Theory
Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…
A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing…
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an…
Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining…
Kuroda's translation embeds classical first-order logic into intuitionistic logic, through the insertion of double negations. Recently, Brown and Rizkallah extended this translation to higher-order logic. In this paper, we adapt it for…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties.…
Combining the representations of the words that make up a sentence into a cohesive whole is difficult, since it needs to account for the order of words, and to establish how the words present relate to each other. The solution we propose…
Compositional vector space models of meaning promise new solutions to stubborn language understanding problems. This paper makes two contributions toward this end: (i) it uses automatically-extracted paraphrase examples as a source of…
The synthesis of string transformation programs from input-output examples utilizes various techniques, all based on an inductive bias that comprises a restricted set of basic operators to be combined. A new algorithm, Transduce, is…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
Reasoning systems with too simple a model of the world and human intent are unable to consider potential negative side effects of their actions and modify their plans to avoid them (e.g., avoiding potential errors). However, hand-encoding…
The goal of this project is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machine-translation methods, (ii) to…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…
Representing meaning in the form of high dimensional vectors is a common and powerful tool in biologically inspired architectures. While the meaning of a set of concepts can be summarized by taking a (possibly weighted) sum of their…