Abstract Inspired by the ”thinking fast and slow” cognitive theory of human decision making, we propose a multi-agent cognitive architecture (SOFAI) that is based on ”fast”/”slow” solvers and a metacognitive module. We then present experimental results on the behavior of an instance of this architecture for AI systems that make decisions about navigating in a constrained environment. We show that combining the two decision modalities through a separate metacognitive function allows for higher decision quality with…

Combinatorial games played between two players, called Spoiler and Duplicator, have often been used to capture syntactic properties of formal logical languages. For instance, the widely used Ehrenfeucht-Fraïssé (EF) game captures the syntactic measure of quantifier rank of first-order formulas. For every such game, there is an associated natural decision problem: "given an instance of the game, does Spoiler win the game on that instance?" For EF games, this problem was shown to be PSPACE-complete by Pezzoli in 199…

Machine-assisted methods for discovering new physical laws of nature, starting from a given background theory and data, have recently emerged, and seem to hold the promise of someday advancing our understanding of the physical world. To address these needs, we have developed SynPAT, a system for generating synthetic physical theories comprising (i) a set of consistent axioms, (ii) a symbolic expression that is a consequence of the axioms and the challenge to be discovered, and (iii) noisy data that approximately m…

We study multi-structural games, played on two sets $\mathcal{A}$ and $\mathcal{B}$ of structures. These games generalize Ehrenfeucht-Fra\"{i}ss\'{e} games. Whereas Ehrenfeucht-Fra\"{i}ss\'{e} games capture the quantifier rank of a first-order sentence, multi-structural games capture the number of quantifiers, in the sense that Spoiler wins the $r$-round game if and only if there is a first-order sentence $\phi$ with at most $r$ quantifiers, where every structure in $\mathcal{A}$ satisfies $\phi$…

The number of quantifiers needed to express first-order properties is captured by two-player combinatorial games called multi-structural (MS) games. We play these games on linear orders and strings, and introduce a technique we call "parallel play", that dramatically reduces the number of quantifiers needed in many cases. Linear orders and strings are the most basic representatives of ordered structures -- a class of structures that has historically been notoriously difficult to analyze. Yet, in this paper, we pro…