On Automating the Doctrine of Double Effect

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.Comment: 26th International Joint Conference on Artificial Intelligence 2017; Special Track on AI & Autonom

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201

Learning-Assisted Automated Reasoning with Flyspeck

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide range of mathematical queries automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39% of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions