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The challenge of creating interpretable models has been taken up by two main research communities: ML researchers primarily focused on lower-level explainability methods that suit the needs of engineers, and HCI researchers who have more…

We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new…

A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…

Recently, several methods have leveraged deep generative modeling to produce example-based explanations of image classifiers. Despite producing visually stunning results, these methods are largely disconnected from classical explainability…

In abstract argumentation theory, many argumentation semantics have been proposed for evaluating argumentation frameworks. This paper is based on the following research question: Which semantics corresponds well to what humans consider a…

The concept of emergence is critically analyzed in particular with respect to the assumed emergence of mental properties from a neuronal basis. We argue that so-called contextual emergence is needed to avoid an eliminatory reductionism.…

Language Models (LMs) have emerged as powerful sources of evidence for linguists seeking to develop theories of syntax. In this paper, we argue that causal interpretability methods, applied to LMs, can greatly enhance the value of such…

By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that PI is irrational". One is…

The standard model of particle physics is marvelously successful. However, it is obviously not a complete or final theory. I shall argue here that the structure of the standard model gives some quite concrete, compelling hints regarding…

We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.

Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…

In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…

We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…

Assurance arguments provide a clear and structured way to explain why stakeholders should trust that a system satisfies certain properties, yet widely used notations, e.g.Goal Structuring Notation (GSN), typically lack an operational…

Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

I discuss two approaches to monotonic proof-theoretic semantics. In the first one, which I call SVA, consequence is understood in terms of existence of valid arguments. The latter involve the notions of argument structure and justification…

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…