Related papers: Intensional Kleene and Rice Theorems for Abstract …
The ability to abstract, count, and use System~2 reasoning are well-known manifestations of intelligence and understanding. In this paper, we argue, using the example of the ``Look and Say" puzzle, that although deep neural networks can…
Commutativity of program code (i.e. the equivalence of two code fragments composed in alternate orders) is of ongoing interest in many settings such as program verification, scalable concurrency, and security analysis. While some have…
We examine the meaning and the complexity of probabilistic logic programs that consist of a set of rules and a set of independent probabilistic facts (that is, programs based on Sato's distribution semantics). We focus on two semantics,…
This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
This paper draws attention to the potential of computational methods in reworking data generated in past qualitative studies. While qualitative inquiries often produce rich data through rigorous and resource-intensive processes, much of…
A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…
We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of…
The impressive performance of recent language models across a wide range of tasks suggests that they possess a degree of abstract reasoning skills. Are these skills general and transferable, or specialized to specific tasks seen during…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of…
An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions. This is a common abstraction used in equivalence checking, compiler optimization, and program verification. While simple, the…
The system PL permits the translation of abstract proofs of program correctness into programs in a variety of programming languages. A programming language satisfying certain axioms may be the target of such a translation. The system PL…
Reinforcement Learning (RL) can enable agents to learn complex tasks. However, it is difficult to interpret the knowledge and reuse it across tasks. Inductive biases can address such issues by explicitly providing generic yet useful…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions…
Examples of discontinuous functions already appear in the work of Euler, Abel, Dirichlet, Fourier, and Bolzano. A ground-breaking discovery due to Baire was that many discontinuous functions are well-behaved in that they are the pointwise…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…