Related papers: On Quantified Modal Theorem Proving for Modeling E…

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…

This paper proposes a basic proof theoretic framework for major modal logics: {\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\sf…

Critical decision-making in socially consequential spaces is increasingly involving AI systems at varying capacities. Yet, despite the ubiquity of autonomous systems, most approaches to handling autonomous moral decision-making resort to…

We consider modal logic extended with the well-known temporal operator 'eventually' and provide a cut-elimination procedure for a cyclic sequent calculus that captures this fragment. The work showcases an adaptation of the reductive…

Many legal computations, including the amount of tax owed by a citizen, whether they are eligible to social benefits, or the wages due to civil state servants, are specified by computational laws. Their application, however, is performed by…

We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…

We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. QE dates back to Tarski's work in the 1940s with software to perform it dating to the 1970s. There is a great body of work considering its…

This paper develops stable canonical rules for intuitionistic modal logics, which were first introduced for superintuitionistic logics and transitive nor mal modal logics in [1] and [2] respectively. We first prove that every in…

This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static)…

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…

Automated commonsense reasoning is essential for building human-like AI systems featuring, for example, explainable AI. Event Calculus (EC) is a family of formalisms that model commonsense reasoning with a sound, logical basis. Previous…

We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…

In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the…

Case studies are typically used to teach 'ethics', but in quantitative courses it can seem distracting, for both instructor and learner, to introduce a case analysis. Moreover, case analyses are typically focused on issues relating to…

We demonstrate how easy it is for modern machine-learned systems to violate common deontological ethical principles and social norms such as "favor the less fortunate," and "do not penalize good attributes." We propose that in some cases…

In this paper we use display calculus to show the decidability for normal modal logic K and some of its extensions.

Epistemic and doxastic logics are modal logics for knowledge and belief, and serve as foundational models for rational agents in game theory, philosophy, and computer science. We examine the consequences of modeling agents capable of a…

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a…

An ethical value-action gap exists when there is a discrepancy between intentions and actions. This discrepancy may be caused by social and structural obstacles as well as cognitive biases. Computational models of cognition and affect can…

Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…