Tractable Reasoning in Knowledge Representation Systems

This document addresses some problems raised by the well-known intractability of deductive reasoning in even moderately expressive knowledge representation systems. Starting from boolean constraint propagation (BCP), a previously known linear-time incomplete reasoner for clausal propositional theories, we develop fact propagation (FP) to deal with non-clausal theories, after motivating the need for such an extension. FP is specified using a confluent rewriting systems, for which we present an algorithm that has quadratic-time complexity in general, but is still linear-time for clausal theories. FP is the only known tractable extension of BCP to non-clausal theories; we prove that it performs strictly more inferences than CNF-BCP, a previously-proposed extension of BCP to non-clausal theories. We generalize a refutation reasoner based on FP to a family of sound and tractable reasoners that are "increasingly complete" for propositional theories. These can be used for anytime reasoning, i.e. they provide partial answers even if they are stopped prematurely, and the "completeness" of the answer improves with the time used in computing it. A fixpoint construction based on FP gives an alternate characterization of the reasoners in this family, and is used to define a transformation of arbitrary theories into logically-equivalent "vivid" theories -- ones for which our FP algorithm is complete. Our final contribution is to the description of tractable classes of reasoning problems. Based on FP, we develop a new property, called bounded intricacy, which is shared by a variety of tractable classes that were previously presented, for example, in the areas of propositional satisfiability, constraint satisfaction, and OR-databases. Although proving bounded intricacy for these classes requires domain-specific techniques (which are based on the original tractability proofs), bounded intricacy is one more tool available for showing that a family of problems arising in some application is tractable. As we demonstrate in the case of constraint satisfaction and disjunctive logic programs, bounded intricacy can also be used to uncover new tractable classes

Uncertainty in climate science and climate policy

This essay, written by a statistician and a climate scientist, describes our view of the gap that exists between current practice in mainstream climate science, and the practical needs of policymakers charged with exploring possible interventions in the context of climate change. By `mainstream' we mean the type of climate science that dominates in universities and research centres, which we will term `academic' climate science, in contrast to `policy' climate science; aspects of this distinction will become clearer in what follows. In a nutshell, we do not think that academic climate science equips climate scientists to be as helpful as they might be, when involved in climate policy assessment. Partly, we attribute this to an over-investment in high resolution climate simulators, and partly to a culture that is uncomfortable with the inherently subjective nature of climate uncertainty.Comment: submitted as contribution to Conceptual Foundations of ClimateModeling, Winsberg, E. and Lloyd, E., eds., The University of Chicago Pres

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This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the axioms of a dynamic provability logic, which embeds GL within the modal $\mu$-calculus. Via correspondence results between modal logic and the bisimulation-invariant fragment of second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via four models, without a decision as to which model is to be preferred. The first model makes intuition sensitive to hyperintensional topics, i.e. subject matters. The second model is a hyperintensional truthmaker semantics, in particular a novel epistemic two-dimensional truthmaker semantics. The third model is a topic-sensitive non-truthmaker epistemic two-dimensional semantics. The fourth model is a topic-sensitive epistemic two-dimensional truthmaker semantics

Are knowledge ascriptions sensitive to social context?

Plausibly, how much is at stake in some salient practical task can affect how generously people ascribe knowledge of task-relevant facts. There is a metaphysical puzzle about this phenomenon, and an empirical puzzle. Metaphysically: there are competing theories about when and how practical stakes affect whether it is correct to ascribe knowledge. Which of these theories is the right one? Empirically: experimental philosophy has struggled to find a stakes-effect on people’s knowledge ascriptions. Is the alleged phenomenon just a philosopher’s fantasy? I propose a new psychological account of when and why people’s knowledge ascriptions are sensitive to stakes. My hypothesis is motivated by empirical research on how people’s judgements are sensitive to their social context. Specifically, people’s evaluations are sensitive to their ‘psychological distance’ from the scenarios they are considering. When using ‘fixed-evidence probes’, experimental philosophy has found that what’s at stake for a fictional character in a made-up scenario has little or no effect on how participants ascribe knowledge to them. My hypothesis predicts this finding: the scenarios are too ‘psychologically distant’ to participants. Our empirical puzzle is resolved: the stakes-effect often present in the wild won’t be present in vignette studies. (This illustrates a widespread problem with X-phi vignette studies: if people might judge differently in other social contexts, we can’t generalize from the results of these experiments. That is, vignette studies are of doubtful ‘external validity’.) The hypothesis also resolves our metaphysical puzzle. It predicts that people do not ascribe knowledge in a way deemed correct by any of the standard philosophical views, namely classical invariantism, interest-relative invariantism, and contextualism. Our knowledge ascriptions shift around in the way that’s most useful for social beings like us, and this pattern in our judgements can only be endorsed by a genuinely relativist metaphysics for knowledge

Reasoning with minimal models: efficient algorithms and applications

AbstractReasoning with minimal models is at the heart of many knowledge-representation systems. Yet it turns out that this task is formidable, even when very simple theories are considered. In this paper, we introduce the elimination algorithm, which performs, in linear time, minimal model finding and minimal model checking for a significant subclass of positive CNF theories which we call positive head-cycle-free (HCF) theories. We also prove that the task of minimal entailment is easier for positive HCF theories than it is for the class of all positive CNF theories. Finally, we show how variations of the elimination algorithm can be applied to allow queries posed on disjunctive deductive databases and disjunctive default theories to be answered in an efficient way

Philosophical foundations of neuroeconomics: economics and the revolutionary challenge from neuroscience.

This PhD thesis focuses on the philosophical foundations of Neuroeconomics, an innovative research program which combines findings and modelling tools from economics, psychology and neuroscience to account for human choice behaviour. The proponents of Neuroeconomics often manifest the ambition to foster radical modifications in the accounts of choice behaviour developed by its parent disciplines. This enquiry provides a philosophically informed appraisal of the potential for success and the relevance of neuroeconomic research for economics. My central claim is that neuroeconomists can help other economists to build more predictive and explanatory models, yet are unlikely to foster revolutionary modifications in the economic theory of choice. The contents are organized as follows. In chapters 1-2, I present neuroeconomists’ investigative tools, distinguish the most influential approaches to neuroeconomic research and reconstruct the case in favour of a neural enrichment of economic theory. In chapters 3-7, I combine insights from neuro-psychology, economic methodology and philosophy of science to develop a systematic critique of Neuroeconomics. In particular, I articulate four lines of argument to demonstrate that economists are provisionally justified in retaining a methodologically distinctive approach to the modelling of decision making. My first argument points to several evidential and epistemological concerns which complicate the interpretation of neural data and cast doubt on the inferences neuroeconomists often make in their studies. My second argument aims to show that the trade-offs between the modelling desiderata that neuroeconomists and other economists respectively value severely constrain the incorporation of neural insights into economic models. My third argument questions neuroeconomists’ attempts to develop a unified theory of choice behaviour by identifying some central issues on which they hold contrasting positions. My fourth argument differentiates various senses of the term ‘revolution’ and illustrates that neuroeconomists are unlikely to provide revolutionary contributions to economic theory in any of these senses