Vincent C. Muller Editor · Computing and Philosophy Selected Papers from IACAP 2014 ~Springer Editor Vincent C. Muller Anatolia College/ACT Thessaloniki, Greece http:l/orcid.org/0000-0002-4144-4957 http://www.sophia.de Synthese Library ISBN 978-3-319-23290-4 ISBN 978-3-319-23291-1 (eBook) DOI 10.1007/978-3-319-23291-1 Library of Congress Control Number: 2015959017 Springer Cham Heidelberg New York Dordrecht London ©Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com) Chapter 8 Introducing the Doxastically Centered Approach to Formalizing Relevance Bonds in Conditionals Selmer Bringsjord, John Licato, Daniel Arista, Naveen Sundar Govindarajulu, and Paul F. Bello Abstract Conditional reasoning is an important part of sophisticated cognition. Such reasoning is systematically studied in the sub-discipline of conditional logic, where the focus has been on the objects over which conditional reasoning operates (formulae, and the internals thereof). We introduce herein a new approach: one marked by a focus on the mental attitudes of the agents engaged in conditional reasoning. We specifically present our approach in connection with the challenge of rigorously capturing what seems to many to be a requiJ:ement for an adequate formalization of conditional reasoning: viz., that the antecedent and consequent in conditionals be relevant to each other. 8.1 Introduction artd Plan Every intelligent autonomous agent must presumably employ some form of con­ ditional reasoning if it is to thrive in its environment. Even the third author's dog seems aided by the faculty to carry out such reasoning. Suppose Rupert is called from the tub to come over. He certainly seems to know that his corning (x), combined with the conditional that if he does he's likely to endure his least­ favorite chore (geting a bath = {3), implies that he will receive a bath. Isn't that The RPI contingent is greatly indebted to the Office of Naval Research for funding to Bringsjord, and all authors deeply appreciate the opportunity for Arista to present on conditional reasoning and relevance atIACAP 2014. In addition, the authors wish to express their gratitude to two anonymous referees for their penetrating comments, criticisms, and suggestions. Finally, the authors are deeply grateful for the leadership, guidance, wisdom, and diligence of editor Vincent Miiller. S. Bringsjord ([BJ) • J. Licato • D. Arista• N.S. Govindarajulu Rensselaer Al & Reasoning (RA!R) Laboratory, Department of Cognitive Science, Department of Computer Science, Rensselaer Polytechnic Institute (RPI), Troy, NY 12180, USA e-mail: [email protected] P.F. Bello Naval Research Laboratory, 4555 Overlook Ave. SW, Washington, DC 20375, USA e-mail: [email protected] ©Springer International Publishing Switzerland 2016 117 V.C. Muller (ed.), Computing and Philosophy, Synthese Library 375, DOI 10.1007/978-3-319-23291-1_8 118 S. Bringsjord et al. why he stares at his master and the tub from a distance, and stays right where he is? Unfortunately, as is well known, it has proved remarkably difficult to suitably model, formally, particular forms of conditionals used in reasoning carried out by intelligent autonomous agents of the biological variety, so that insight can be gained as to how one of the silicon variety, e.g. a smart robot, can be engineered.1 Empirical confirmation comes from many sources; one is the lack of consensus, in the sub­ discipline of conditional logic (classicapy introduced by Nute 1984), as to how the many types of conditionals out there in the minds and discourse of humans, are to be formalized. One of the chief, specific challenges cunently blocking such consensus, and the challenge we focus upon in this short chapter, is that of figuring out how to ensure relevance between antecedent and consequent in conditionals. For example, if --+ is the material conditional, one might model our canine example by some such sequence as x x--+ fJ .·. fJ modus ponens But once we adopt this model we must accept the consequence that for any proposition 1j; believed by Rupert, he can justify the belief that anything else he believes, or even arbitrarily assumes, implies 1j; .2 That seems rather implausible. Surely Rupert's reasoning about bath time involves some kind of intuitive relevance between x and .{J_. And this is all the more true at the human level, of course. In short, relevance ieems to be a crucial part of what binds the dyads of conditional reasoning. But what does the relevance between these dyads consist in? The pioneers of relevance logic, as well as their intellectual descendants, have looked for relevance in certain relationships between formulae, elements thereof (e.g., variables, relations, etc.), and meta-structures built from assembling and arranging such formulae. This approach is seen to be followed time and time again in any comprehensive survey of relevance logic; for example, see the masterful survey provided in Mares (2014). For example, the pioneers provided systems in which such formula-schemas as 1At the dawn of AI, Herb Simon blithely took Principia Mathematica's material conditional off the shelf, and charged ahead in building LOGIC THEORIST (which, to much fanfare, automatically proved theorems from PM), and in declaring that human-level machine intelligence was just around the corner. Simon was of course rather too sanguine; and part of the problem, by our lights, was the "irrelevant" conditional he affirmed, without modeling the mental attitudes of relevant agents. (Yet the employment of formal logic as the vehicle of choice was wise.) 2This is implied by the theorem below, in conjuction with mild assumptions about canine epistemology quite outside the present investigation. That investigation centers on humans and human-level agents/robots, not dogs. 8 Introducing the Doxastically Centered Approach to Formalizing Relevance ... 119 are not theorems. (This is of course an easy theorem in the standard propositional calculus.) But the clever blocks of such theorems were, and still are, far from the ra­ tiocination ofreal and robust agents, and appear to be but syntactic prestidigitation, not moves that lead to the real engineering of real robots with the kind of flexible thinking that is needed in order to thrive in the real world. Accordingly, we introduce herein a new approach to the relevance in conditionals, one that takes explicit account of the mental attitudes of agents, and isn't limited only to deduction, and variants thereof, but rather includes analogical reasoning. We classify our approach as doxastically centered, because it explicitly factors in the beliefs of the agents doing the reasoning. The sequel unfolds as follows. Next (Sect. 8:2), we give a brief overview of the expressive intensional logic that serves as the backbone of our new approach to relevance. We then (Sect. 8.3) first present our doxastically centered approach in the context of analogical reasoning, in connection, specifically, with subjunctive conditionals (Sect. 8.3). Next, in Sect. 8.4, we present our doxastically centered approach in connection with deductive reasoning, with special attention paid to material and so-called "strict" conditionals, but where the type of conditionals in question can in principle vary across all the types studied in-conditional logic. A brief conclusion wraps up the paper. 8.2 Quick Overview of 'lJC'EC* Our new approach to formalizing and mechanizing relevance is built upon the foun­ dation of a well-established, computational, implemented first-order multi-modal logic, the deontic cognitive event calculus ('DC'EC*) (Bringsjord and Govindarajulu 2013; Bringsjord et al. 2014). 'IJC'EC* is extremely expressive, in that regard well beyond even expressive extensional logics like first- or second-order logic (FOL, SOL), and a fortiori beyond the FOL-based Event Calculus axiom system (Kowalski and Sergot 1986) subsumed by 'IJC'EC* (and used to model and track time and change), and indeed beyond traditional so-called "BDI" logics, as explained in Arkoudas and Bringsjord (2009). At least by the standards of philosophy of mind, merely propositional multi-modal logics are just not sufficiently expressive, and therefore 'lJC'EC* is quantificational. For instance, such propositional logics cannot capture the difference between de dicto c~ "believing that" simpliciter), de re c~ "believing of some x that"), and de se c~ "believing of oneself that") belief; yet all three are crucial in philosophically sophisticated modeling of the human mind (Bringsjord and Govindarajulu 2012; Chisholm 1976). (The * in ''])C'EC*' is a reflection of our following philosopher Castaneda (1999) on self-consciousness.) The versatility of first-order logic is very convenient, and is further augmented by such 'IJC'EC* intensional constructs such as common knowledge, communication, and perception. In addition, 'DC'EC* has a proof-theoretic semantics, as explained and defended in Bringsjord et al.