Related papers: Generating collection transformations from proofs

In task-oriented conversation systems, natural language generation systems that generate sentences with specific information related to conversation flow are useful. Our study focuses on language generation by considering various…

Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…

When people interpret text, they rely on inferences that go beyond the observed language itself. Inspired by this observation, we introduce a method for the analysis of text that takes implicitly communicated content explicitly into…

In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…

Strictly positive logics recently attracted attention both in the description logic and in the provability logic communities for their combination of efficiency and sufficient expressivity. The language of Reflection Calculus RC consists of…

Natural language definitions possess a recursive, self-explanatory semantic structure that can support representation learning methods able to preserve explicit conceptual relations and constraints in the latent space. This paper presents a…

We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of…

An emerging computing paradigm, so-called next-generation reservoir computing (NG-RC) is investigated. True to its namesake, NG-RC requires no actual reservoirs for input data mixing but rather computing the polynomial terms directly from…

We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…

We study the interpretability issue of task-oriented dialogue systems in this paper. Previously, most neural-based task-oriented dialogue systems employ an implicit reasoning strategy that makes the model predictions uninterpretable to…

Continuous representations of logic formulae allow us to integrate symbolic knowledge into data-driven learning algorithms. If such embeddings are semantically consistent, i.e. if similar specifications are mapped into nearby vectors, they…

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…

It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…

How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic…

In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…

The distributed representations currently used are dense and uninterpretable, leading to interpretations that themselves are relative, overcomplete, and hard to interpret. We propose a method that transforms these word vectors into reduced…

Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…

We build a dual-way neural dictionary to retrieve words given definitions, and produce definitions for queried words. The model learns the two tasks simultaneously and handles unknown words via embeddings. It casts a word or a definition to…

Reasoning, a crucial aspect of NLP research, has not been adequately addressed by prevailing models including Large Language Model. Conversation reasoning, as a critical component of it, remains largely unexplored due to the absence of a…

The Refinement Calculus of Reactive Systems (RCRS) is a compositional formal framework for modeling and reasoning about reactive systems. RCRS provides a language which allows to describe atomic components as symbolic transition systems or…