Related papers: Teaching Functional Programmers Logic and Metatheo…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics…
A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm,…
While neural networks are good at learning unspecified functions from training samples, they cannot be directly implemented in hardware and are often not interpretable or formally verifiable. On the other hand, logic circuits are…
Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical…
Formal programming language semantics are imperative when trying to verify properties of programs in an automated manner. Using a new approach, Din et al. strengthen the ability of reasoning about concurrent programs by proposing a modular…
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
Learning complex programs through inductive logic programming (ILP) remains a formidable challenge. Existing higher-order enabled ILP systems show improved accuracy and learning performance, though remain hampered by the limitations of the…
Belief revision has been studied mainly with respect to background logics that are monotonic in character. In this paper we study belief revision when the underlying logic is non-monotonic instead--an inherently interesting problem that is…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
Introducing inner-city high school students to program design presents unique challenges. The typical assumptions of an introductory programming course, like students understand what variables and functions are, may not be safe. Therefore,…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
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…
Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Learning from Demonstration~(LfD) should capture not only how a task is executed, but also its high-level task structure that explains the demonstrated behavior. As robots become more autonomous, such task representations must be…
Formal learning theory formalizes the process of inferring a general result from examples, as in the case of inferring grammars from sentences when learning a language. Although empirical evidence suggests that children can learn a language…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
In systems verification we are often concerned with multiple, inter-dependent properties that a program must satisfy. To prove that a program satisfies a given property, the correctness of intermediate states of the program must be…
Oz is a multiparadigm language that supports logic programming as one of its major paradigms. A multiparadigm language is designed to support different programming paradigms (logic, functional, constraint, object-oriented, sequential,…