Related papers: The Formalization of Syntax-Based Mathematical Alg…

In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…

We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…

The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…

functionalObjects.h allows the C++ programmer performing common mathematical calculations to use a more symbolic syntax rather than an algorithmic syntax. This is not as ambitious as a symbolic manipulation program such as Mathematica; it…

We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…

Framing involves the positive or negative presentation of an argument or issue depending on the audience and goal of the speaker (Entman 1983). Differences in lexical framing, the focus of our work, can have large effects on peoples'…

Word representations induced from models with discrete latent variables (e.g.\ HMMs) have been shown to be beneficial in many NLP applications. In this work, we exploit labeled syntactic dependency trees and formalize the induction problem…

Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…

We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…

We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…

One major problem in Natural Language Processing is the automatic analysis and representation of human language. Human language is ambiguous and deeper understanding of semantics and creating human-to-machine interaction have required an…

We provide a novel notion of what it means to be interpretable, looking past the usual association with human understanding. Our key insight is that interpretability is not an absolute concept and so we define it relative to a target model,…

Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for…

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications,…

Program synthesis is the generation of a program from a specification. Correct synthesis is difficult, and methods that provide formal guarantees suffer from scalability issues. On the other hand, neural networks are able to generate…

The author describes a conceptual study towards mapping grounded natural language discourse representation structures to instances of controlled language statements. This can be achieved via a pipeline of preexisting state of the art…

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…

One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…

Code generation, defined as automatically writing a piece of code to solve a given problem for which an evaluation function exists, is a classic hard AI problem. Its general form, writing code using a general language used by human…