Related papers: Beyond the Elementary Representations of Program I…
The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
It has been found that Transformer-based language models have the ability to perform basic quantitative reasoning. In this paper, we propose a method for studying how these models internally represent numerical data, and use our proposal to…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
Data trees are trees in which each node, besides carrying a label from a finite alphabet, also carries a data value from an infinite domain. They have been used as an abstraction model for reasoning tasks on {XML} and verification. However,…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindstr\"om quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
We explore different ways of implementing temporal constraints expressed in an extension of Answer Set Programming (ASP) with language constructs from dynamic logic. Foremost, we investigate how automata can be used for enforcing such…
Classical models for supervised machine learning, such as decision trees, are efficient and interpretable predictors, but their quality is highly dependent on the particular choice of input features. Although neural networks can learn…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
We consider sets/relations/computations defined by *Elementary Inference Systems* I, which are obtained from Smullyan's *elementary formal systems* using Gentzen's notation for inference rules, and proof trees for atoms P(t_1,...,t_n),…
Predicting program properties such as names or expression types has a wide range of applications. It can ease the task of programming and increase programmer productivity. A major challenge when learning from programs is $\textit{how to…
Both hybrid automata and action languages are formalisms for describing the evolution of dynamic systems. This paper establishes a formal relationship between them. We show how to succinctly represent hybrid automata in an action language…