Related papers: Logic-Based Artificial Intelligence Algorithms Sup…
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Artificial Intelligence models are becoming increasingly more powerful and accurate, supporting or even replacing humans' decision making. But with increased power and accuracy also comes higher complexity, making it hard for users to…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
The need to explain the output from Machine Learning systems designed to predict the outcomes of legal cases has led to a renewed interest in the explanations offered by traditional AI and Law systems, especially those using factor based…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
The overarching goal of Explainable AI is to develop systems that not only exhibit intelligent behaviours, but also are able to explain their rationale and reveal insights. In explainable machine learning, methods that produce a high level…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
Of primary importance in formulating a response to the increasing prevalence and power of artificial intelligence (AI) applications in society are questions of ontology. Questions such as: What "are" these systems? How are they to be…
There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
We aim to accelerate the original vision of the semantic web by revisiting design decisions that have defined the semantic web up until now. We propose a shift in direction that more broadly embraces existing data infrastructure by…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…