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Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour…
This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the $\invertediota$ operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas…
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member,…
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…
As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
While utilization of digital agents to support crucial decision making is increasing, trust in suggestions made by these agents is hard to achieve. However, it is essential to profit from their application, resulting in a need for…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Knowing the norms of a domain is crucial, but there exist no repository of norms. We propose a method to extract them from texts: texts generally do not describe a norm, but rather how a state-of-affairs differs from it. Answers concerning…
To build intelligent machine learning systems, there are two broad approaches. One approach is to build inherently interpretable models, as endeavored by the growing field of causal representation learning. The other approach is to build…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
Theory and empirical science should be in constant dialogue, but often find it hard to understand one another. Here we describe a graduate-level university course we developed to improve matters. The course was designed to help…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
We are aiming at a semantics of logic programs with preferences defined on rules, which always selects a preferred answer set, if there is a non-empty set of (standard) answer sets of the given program. It is shown in a seminal paper by…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of "forward induction," because rational agents may use dominated strategies as experiments to learn how opponents play,…
The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…