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Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…

In the area of computer science focusing on creating machines that can engage on behaviors that humans consider intelligent. The ability to create intelligent machines has intrigued humans since ancient times and today with the advent of…

Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…

The process of cognition is analysed to adjust the set theory to physical description. Postulates and basic definitions are revised. The specific sets of predicates, called presets, corresponding to the physical objects identified by an…

The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing concurrency. Central to this…

We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…

Pattern matching is a popular feature in functional, imperative and object-oriented programming languages. Language designers should therefore invest effort in a good design for pattern matching. Most languages choose a first-match…

Deep ensembles can be considered as the current state-of-the-art for uncertainty quantification in deep learning. While the approach was originally proposed as a non-Bayesian technique, arguments supporting its Bayesian footing have been…

In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian…

We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles…

A classical result by Floyd ("On the non-existence of a phrase structure grammar for ALGOL 60", 1962) states that the complete syntax of any sensible programming language cannot be described by the ordinary kind of formal grammars…

This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define…

We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by Brass…

Despite the fact that beliefs are mental states that cannot be directly observed, humans talk about each others' beliefs on a regular basis, often using rich compositional language to describe what others think and know. What explains this…

In this chapter we discuss the problem of enumerating distinct regular expressions by size and the regular languages they represent. We discuss various notions of the size of a regular expression that appear in the literature and their…

We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…

In this paper we examine two ways of coding sequences in arithmetical theories. We investigate under what conditions they work. To be more precise, we study the creation of objects of a data-type that we call ur-strings, roughly sequences…

Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall…

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…