Nuclear deterrence and the logic of deliberative mindreading

Abstract

Although the computational modeling of “mindreading” (e.g., believing that you believe that there’s a deadly boa in the box, Smith mindreadingly predicts that you will refrain from removing the top) is well-established, this success has been achieved primarily in connection with scenarios that, relatively speaking, are both simple and common. Herein, we introduce a new computational-logic framework that allows formalization of mindreading of a rather more demanding sort: viz., deliberative multi-agent mindreading, applied to the realm of nuclear strategy. This form of mindreading, in this domain, is both complex and uncommon: it for example can quickly involve at least formulae reflecting fifth-order beliefs, and requires precise deductive reasoning over such iterated beliefs. In addition, the relevant models and simulations involve three, four, five agents, and sometimes many more. In the nuclear-strategy realm, for example, the better kind of modeling, simulation, and prediction (MSP) that our framework is intended to enable, should ultimately be capable of formalizing, at once, the arbitrarily iterated beliefs of at least every civilized nation on Earth. Based on our modeling, we present a set of desiderata that any modeling framework should satisy to be able to capture deliberative multi-agent mindreading in domains such as nuclear deterrence. Using our desiderata, we evaluate game theory, metagame theory, digital games, and tabletop games when used to model nuclear deterrence. Finally, we consider and rebut possible objections to our modeling paradigm and conclude with a map of ongoing and future work.

Introduction

The computational modeling of “mindreading” (e.g., believing that you believe that there’s a deadly boa in the box, Smith mindreadingly predicts that you will refrain from removing the top) is well-established (e.g., see Arkoudas and Bringsjord, 2009, Bello et al., 2007). However, past success has been achieved in connection with scenarios that, relatively speaking, are both simple and common. Consider for instance the false-belief scenario, which drives both of (Arkoudas and Bringsjord, 2009, Bello et al., 2007); a scenario in which a young child, or the computational agent serving as a simulacrum thereof, must predict where some other agent will look in order to retrieve an object from b. A successful prediction requires that the child believe that the other agent believes that the object is located in b. Everyday life, from toddlerhood to (lucid) senescence, is filled with the need to make such predictions in such two-agent cases, on the strength of such second-order beliefs. You do not need a snake and a box or other contrivances to exemplify the logical relationships: If Jones is standing beside Smith while the latter is cooking a meal, and the former is considerate, Jones will not want to be located so as to block Smith’s removal of now-grilled chorizo from one pan in order to add it to the sauce in another—and the courtesy of Jones inheres in his second-order belief about what Smith believes. In addition, both the number and average syntactic complexity of the formulas required to model such scenarios is relatively small.

Herein, we introduce a new computational-logic framework that allows formalization of mindreading of a rather more demanding sort: viz., deliberative multi-agent mindreading, applied to the realm of nuclear strategy. This form of mindreading, in this domain, is both complex and uncommon: it for example can quickly involve at least formulae reflecting fifth-order beliefs, and requires precise deductive reasoning over such iterated beliefs. In addition, the relevant models and simulations involve three, four, five agents, and sometimes many more. In the nuclear-strategy realm, for example, the better kind of modeling, simulation, and prediction (MSP) that our framework is intended to enable, should ultimately be capable of formalizing, at once, the arbitrarily iterated beliefs of at least every civilized nation on Earth.

Our plan for the present paper: In the next section (Section 2), we use a highly expressive intensional logic $({\mathcal{DCEC}}^{\ast })$, embedded within a turnstyle rubric, to model, in four increasingly robust ways, snapshots taken of a four-agent, real-world interaction relating to nuclear deterrence. (The four agents are idealized representatives of the U.S., Israel, Iran, and Russia.) As we explain, this modeling is undertaken with the purpose of achieving simulations that enable predictions about the future, conditional on what actions are performed before at least the end of the future to be charted. In Section 3, we use and extend our modeling in Section 2 to prove that the U.S.’s applying severe economic sanctions, under certain reasonable suppositions, will not deter Iran from working toward massive first-strike capability against Israel. After taking stock of the eight chief advantages of (= desiderata derived from) our modeling approach (Section 4), we explain that both modern digital and tabletop games, and game and metagame theory, are inadequate as a basis for such modeling (Section 5). Next, we anticipate and rebut a series of objections to our new paradigm (Section 6). Finally, in a brief concluding section, we point toward our ongoing and future work.