Related papers: Towards a formalization of budgets
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
People often plan hierarchically. That is, rather than planning over a monolithic representation of a task, they decompose the task into simpler subtasks and then plan to accomplish those. Although much work explores how people decompose…
This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
To conduct a didactic analysis of the current modality of study of real numbers in the Bachelor's Degree in Mathematics, we rely on the notion of didactic paradigm and employ a novel research methodology within the framework of the…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
People rationalize their past choices, even those that were mistakes in hindsight. We propose a formal theory of this behavior. The theory predicts that sunk costs affect later choices. Its model primitives are identified by choice behavior…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…
Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
Recently, a new wave of thinking-capable Large Language Models has emerged, demonstrating exceptional capabilities across a wide range of reasoning benchmarks. Early studies have begun to explore how the amount of compute in terms of the…
Quantum resource theory is a cutting-edge tool used to study practical implementations of quantum mechanical principles under realistic operational constraints. It does this by modelling quantum systems as restricted classes of possible or…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…
This expository paper is concerned with the rationality problems for three-dimensional algebraic varieties with a conic bundle structure. We discuss the main methods of this theory. We sketch the proofs of certain principal results, and…
We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques -- as those popular in process calculi -- we extend classical regular expressions with names (to model…