Related papers: Towards Specifying Symbolic Computation
This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…
For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely…
An expression is any mathematical formula that contains certain formal variables and operations to be executed in a specified order. In computer science, it is usually convenient to represent each expression in the form of an expression…
This paper proposes a framework for computational modeling of artistic painting algorithms, inspired by human creative practices. Based on examples from expert artists and from the author's own experience, the paper argues that creative…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
Before we can get the whole potential of employing computers in the process of managing mathematical `knowledge', we have to convert informal knowledge into machine-oriented representations. How exactly to support this process so that it…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
In this paper, we present a new approach to the semantic enrichment of mathematical expression problem. Our approach is a combination of statistical machine translation and disambiguation which makes use of surrounding text of the…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…
A recommendation system assists users in finding items that are relevant to them. Existing recommendation models are primarily based on predicting relationships between users and items and use complex matching models or incorporate…
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…
The semantic technologies pose new challenge for the way in which we built and operate systems. They are tools used to represent significances, associations, theories, separated from data and code. Their goal is to create, to discover, to…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…