Cut-free Calculi and Relational Semantics for Temporal STIT Logics

arXiv.org Artificial Intelligence

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm, Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3TSTIT are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also XSTIT can be characterized through relational frames, omitting the use of BT+AC frames.


Designing Normative Theories of Ethical Reasoning: Formal Framework, Methodology, and Tool Support

arXiv.org Artificial Intelligence

The area of formal ethics is experiencing a shift from a unique or standard approach to normative reasoning, as exemplified by so-called standard deontic logic, to a variety of application-specific theories. However, the adequate handling of normative concepts such as obligation, permission, prohibition, and moral commitment is challenging, as illustrated by the notorious paradoxes of deontic logic. In this article we introduce an approach to design and evaluate theories of normative reasoning. In particular, we present a formal framework based on higher-order logic, a design methodology, and we discuss tool support. Moreover, we illustrate the approach using an example of an implementation, we demonstrate different ways of using it, and we discuss how the design of normative theories is now made accessible to non-specialist users and developers.


The Temporal Analysis of Chisholm's Paradox

AAAI Conferences

Box 1738 3000 DR Rotterdam, the Netherlands YTANQFAC.FBK.EUR..NL Abstract Deontic logic, the logic of obligations and permissions, is plagued by several paradoxes that have to be understood before deontic logic can be used as a knowledge representation language. In this paper we extend the temporal analysis of Chishohn's paradox using a deontic logic that combines temporal and preferential notions. Introduction Deontic logic is a modal logic in which Op is read as'p ought to be (done).' Deontic logic has traditionally been used by philosophers to analyze the structure of the normative use of language. In the eighties deontic logic had a revival, when it was discovered by computer scientists that this logic can be used for the formal specification and validation of a wide variety of topics in computer science (for an overview and further references see (Wieringa & Meyer 1993)). The advantage is that norms can be violated without creating an inconsistency in the formal specification, in contrast to violations of hard constraints. Another application is the use of deontic logic to represent legal reasoning in legal expert systems in artificial intelligence. Legal expert systems have to be able to reason about legal rules and documents such as for example a trade contract.


On Quantified Modal Theorem Proving for Modeling Ethics

arXiv.org Artificial Intelligence

Second International Workshop on Automated Reasoning: Challenges, Applications, Directions, Exemplary Achievements (ARCADE 2019) EPTCS 311, 2019, pp. In the last decade, formal logics have been used to model a wide range of ethical theories and principles with the goal of using these models within autonomous systems. Logics for modeling ethical theories, and their automated reasoners, have requirements that are different from modal logics used for other purposes, e.g. for temporal reasoning. Particularly, a quantified modal logic, the deontic cognitive event calculus (DC E C), has been used to model various versions of the doctrine of double effect, akrasia, and virtue ethics. Using a fragment of DC E C, we outline these distinct characteristics and present a sketches of an algorithm that can help with some aspects proof automation forDC E C . 1 Introduction Modal logics have been used for decades to model and study a diverse set of subjects -- e.g.


On Automating the Doctrine of Double Effect

arXiv.org Artificial Intelligence

The doctrine of double effect ($\mathcal{DDE}$) is a long-studied ethical principle that governs when actions that have both positive and negative effects are to be allowed. The goal in this paper is to automate $\mathcal{DDE}$. We briefly present $\mathcal{DDE}$, and use a first-order modal logic, the deontic cognitive event calculus, as our framework to formalize the doctrine. We present formalizations of increasingly stronger versions of the principle, including what is known as the doctrine of triple effect. We then use our framework to simulate successfully scenarios that have been used to test for the presence of the principle in human subjects. Our framework can be used in two different modes: One can use it to build $\mathcal{DDE}$-compliant autonomous systems from scratch, or one can use it to verify that a given AI system is $\mathcal{DDE}$-compliant, by applying a $\mathcal{DDE}$ layer on an existing system or model. For the latter mode, the underlying AI system can be built using any architecture (planners, deep neural networks, bayesian networks, knowledge-representation systems, or a hybrid); as long as the system exposes a few parameters in its model, such verification is possible. The role of the $\mathcal{DDE}$ layer here is akin to a (dynamic or static) software verifier that examines existing software modules. Finally, we end by presenting initial work on how one can apply our $\mathcal{DDE}$ layer to the STRIPS-style planning model, and to a modified POMDP model.This is preliminary work to illustrate the feasibility of the second mode, and we hope that our initial sketches can be useful for other researchers in incorporating DDE in their own frameworks.