Though there have been productive interactions between moral philosophers and deontic logicians, there has also been a tradition of neglecting the insights that the fields can offer one another. The most sustained interactions between moral philosophers and deontic logicians have notbeen systematic but instead have been scattered across a number of distinct and often unrelated topics. This chapter primarily focuses on three topics. First, we discuss the “actualism/possibilism” debate which, very roughly, concerns the relevance of what one will do at (...) some future time to what one ought to do at present (§2). This topic is also used to introduce various modal deontic logics. Second we discuss the particularism debate which, very roughly, concerns whether there can be any systematic general theory of what we ought to do (§3). This topic is also used to introduce various non-modal deontic logics. Third, we discuss collective action problems which concern the connection between the obligations of individuals and the behavior and obligations of groups of individuals (§4).This topic is also used to discuss formal systems that allow us to study the relationship between individuals and groups. The chapter also contains a general discussion of the relation between ethical theory and deontic logic (§1) and a brief consideration of other miscellaneous topics (§5). (shrink)

There is consensus among computer scientists, logicians, and philosophers that good reasoning with qualitative beliefs must have the structural property of cumulative transitivity or, for short, cut. This consensus is typically explicitly argued for partially on the basis of practical and mathematical considerations. But the consensus is also implicit in the approach philosophers take to almost every puzzle about reasoning that involves multiple steps: philosophers typically assume that if each step in reasoning is acceptable considered on its own, the whole (...) chain of reasoning must also acceptable. In this paper I focus on whether there are good philosophical reasons for thinking that the consensus that good reasoning must satisfy cut is true. My central claim is that we should not accept the consensus—good reasoning might not satisfy cut. In particular, I consider four arguments for the consensus and explain why they are unpersuasive. (§2-5). I then show that the issue of whether good reasoning is cut turns on a substantive yet until now unnoticed question in epistemology (§6). (shrink)

While the epistemic significance of disagreement has been a popular topic in epistemology for at least a decade, little attention has been paid to logical disagreement. This monograph is meant as a remedy. The text starts with an extensive literature review of the epistemology of (peer) disagreement and sets the stage for an epistemological study of logical disagreement. The guiding thread for the rest of the work is then three distinct readings of the ambiguous term ‘logical disagreement’. Chapters 1 and (...) 2 focus on the Ad Hoc Reading according to which logical disagreements occur when two subjects take incompatible doxastic attitudes toward a specific proposition in or about logic. Chapter 2 presents a new counterexample to the widely discussed Uniqueness Thesis. Chapters 3 and 4 focus on the Theory Choice Reading of ‘logical disagreement’. According to this interpretation, logical disagreements occur at the level of entire logical theories rather than individual entailment-claims. Chapter 4 concerns a key question from the philosophy of logic, viz., how we have epistemic justification for claims about logical consequence. In Chapters 5 and 6 we turn to the Akrasia Reading. On this reading, logical disagreements occur when there is a mismatch between the deductive strength of one’s background logic and the logical theory one prefers (officially). Chapter 6 introduces logical akrasia by analogy to epistemic akrasia and presents a novel dilemma. Chapter 7 revisits the epistemology of peer disagreement and argues that the epistemic significance of central principles from the literature are at best deflated in the context of logical disagreement. The chapter also develops a simple formal model of deep disagreement in Default Logic, relating this to our general discussion of logical disagreement. The monograph ends in an epilogue with some reflections on the potential epistemic significance of convergence in logical theorizing. (shrink)

The informal logic movement began as an attempt to develop – and teach – an alternative logic which can account for the real life arguing that surrounds us in our daily lives – in newspapers and the popular media, political and social commentary, advertising, and interpersonal exchange. The movement was rooted in research and discussion in Canada and especially at the University of Windsor, and has become a branch of argumentation theory which intersects with related traditions and approaches (notably formal (...) logic, rhetoric and dialectics in the form of pragma-dialectics). In this volume, some of the best known contributors to the movement discuss their views and the reasoning and argument which is informal logic’s subject matter. Many themes and issues are explored in a way that will fuel the continued evolution of the field. Federico Puppo adds an insightful essay which considers the origins and development of informal logic and whether informal logicians are properly described as a “school” of thought. In considering that proposition, Puppo introduces readers to a diverse range of essays, some of them previously published, others written specifically for this volume. (shrink)

In this chapter, we begin by sketching in the broadest possible strokes the ideas behind two formal systems that have been introduced with to goal of explicating the ways in which reasons interact to support the actions and conclusions they do. The first of these is the theory of defeasible reasoning developed in the seminal work of Pollock; the second is a more recent theory due to Horty, which adapts and develops the default logic introduced by Reiter to provide an (...) account of reasons. However, the implementations are complex enough, in both cases, to prevent anything more than this sketch. And we would not want to give the impression that we think that work on the logic of reasons must follow the path mapped out in either of these theories—indeed, we feel that the field is wide open. In the remainder of the chapter, therefore, will concentrate on a number of issues bearing on the logic of reasons that are either not treated in the work of Pollock and Horty, or whose treatment there is, we feel, either inadequate or incomplete. These are: first, the question of whether it is necessary to understand logical interactions among reasons themselves, rather than simply between reasons and the actions or conclusions they support, and if so, what principles might govern these interactions; second, priority relations among reasons and the notion of reason accrual; and third, some problems posed by undercutting defeat. (shrink)

The paper presents an exhaustive menu of nonmonotonic logics. The options are individuated in terms of the principles they reject. I locate, e.g., cumulative logics and relevance logics on this menu. I highlight some frequently neglected options, and I argue that these neglected options are particularly attractive for inferentialists.

In the present work we illustrate how two sorts of defeasible reasoning that are fundamental in the normative domain, that is, reasoning about exceptions and reasoning about violations, can be simulated via monotonic propositional theories based on a bimodal language with primitive operators representing knowledge and obligation. The proposed theoretical framework paves the way to using native theorem provers for multimodal logic, such as MleanCoP, in order to automate normative reasoning.

This paper presents an adaptive logic enhancement of conditional logics of normality that allows for defeasible applications of Modus Ponens to conditionals. In addition to the possibilities these logics already offer in terms of reasoning about conditionals, this way they are enriched by the ability to perform default inferencing. The idea is to apply Modus Ponens defeasibly to a conditional and a fact on the condition that it is ‘safe' to do so concerning the factual and conditional knowledge at hand. (...) It is for instance not safe if the given information describes exceptional circumstances: although birds usually fly, penguins are exceptional to this rule. The two adaptive standard strategies are shown to correspond to different intuitions, a skeptical and a credulous reasoning type, which manifest themselves in the handling of so-called floating conclusions. (shrink)

Consistency-based approaches in nonmonotonic reasoning may be expected to yield multiple sets of default conclusions for a given default theory. Reasoning about such extensions is carried out at the meta-level. In this paper, we show how such reasoning may be carried out at the object level for a large class of default theories. Essentially we show how one can translate a default theory Δ, obtaining a second Δ', such that Δ has a single extension that encodes every extension of _. (...) Moreover, our translated theory is only a constant factor larger than the original. We prove that our translation behaves correctly. In the approach we can now encode the notion of extension from within the framework of standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension. This result has some theoretical interest, in that it shows how multiple extensions of semi-monotonic default theories are encodable with manageable overhead in a single extension. (shrink)

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are “syntax- based” or “semantic-based”, “foundational” or “coherentist”, “consistence-restoring” or “inconsistency-tolerant”. Our contribution towards clarifying the connections between these various approaches is threefold: •We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to revision (...) and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. •We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches [BDP95]. •As a direct application of the above, we show that Poole's (syntax-based) system of default reasoning and Shoham's preferential semantic for non monotonic reasoning are also expressively equivalent, in that they can represent the same set of non monotonic consequence relations. (shrink)

This special issue presents a selection of papers in Knowledge Representation in Artificial Intelligence , intended to illustrate the depth and breadth of current research in the area. It comes just over 25 years since a similar special issue of the Journal of Philosophical Logic appeared on the topic Philosophical Logic and Artificial Intelligence [15]. This latter special issue covered work addressing the use of logic, in one form or another, for representing and reasoning with knowledge. The papers of the (...) 1988 special issue give a good indication of major themes of research at the time: reasoning about belief and knowledge [5], tractable logical reasoning [10], nonmonotonicity [11], and reasoning about action [13]. These topics can be considered to be centrally in KR; the current issue then also serves to indicate how the field has broadened and evolved over the last 25 years.Traditionally the area of Knowledge Representation has been seen as “the field of study concerned w .. (shrink)

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

Situational aspects of action are discussed. The presented approach emphasizes the role of situational contexts in which actions are performed. These contexts influence the course of an action; they are determined not only by the current state of the system but also shaped by other factors as time, the previously undertaken actions and their succession, the agents of actions and so on. The distinction between states and situations is explored from the perspective of action systems. The notion of a situational (...) action system is introduced and its theory is expounded. Numerous examples illustrate the reach of the theory. (shrink)

This paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging (...) puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences. (shrink)

Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency—the idea of a defeasible property representing internal conflict of an inductive or evidential nature—has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonotonic inconsistency in terms of nonmonotonic consequence, and a series of results showing that nonmonotonic (...) inconsistency conforms to these postulates given the analysis of nonmonotonic inconsistency presented here and certain postulates for nonmonotonic consequence. The results presented here establish the interest of certain previously undiscussed postulates of nonmonotonic consequence. These results also show that nonmonotonicity, which has never seemed useful in the formulation of general principles governing nonmonotonic reasoning, is relevant to the positive characterization of nonmonotonic inference after all. (shrink)

This paper presents a logical Style painting classifier based on evaluated Horn clauses, qualitative colour descriptors and Explanations. Three versions of $\ell $-SHE are defined, using rational Pavelka logic, and expansions of Gödel logic and product logic with rational constants: RPL, $G$ and $\sqcap $, respectively. We introduce a fuzzy representation of the more representative colour traits for the Baroque, the Impressionism and the Post-Impressionism art styles. The $\ell $-SHE algorithm has been implemented in Swi-Prolog and tested on 90 paintings (...) of the QArt-Dataset and on 247 paintings of the Paintings-91-PIB dataset. The percentages of accuracy obtained in the QArt-Dataset for each $\ell $-SHE version are 73.3%, 65.6% $) and 68.9% $). Regarding the Paintings-91-PIB dataset, the percentages of accuracy obtained for each $\ell $-SHE version are 60.2%, 48.2% $) and 57.0% $). Our logic definition for the Baroque style has obtained the highest accuracy in both datasets, for all the $\ell $-SHE versions. An important feature of the classifier is that it provides reasons regarding why a painting belongs to a certain style. The classifier also provides reasons about why outliers of one art style may belong to another art style, giving a second classification option depending on its membership degrees to these styles. (shrink)

An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...) notion of information-value and therefore the usual economic techniques of optimization cannot be applied in order to compute optimal contractions. But in cases of this sort it is still rational to maximize, i.e. to deem an option as choosable when it is not known to be worse that any other. We present here basic results about a notion of liberal contraction based on maximizing quasi-orderings. This requires the previous solution of some open problems in the theory of rational choice functions, namely a full characterization of choice functions rationalizable in terms of maximization of quasi-transitive relations. We conclude by discussing the problem of what is the adequate feasible set for calculating maximizing solutions for contraction problems and by considering the epistemological roots of some counterexamples against the most fundamental axioms on choice functions (like α). While the first part of the paper shows how economic insights can be used to improve our understanding of the principles of belief formation and change, this final section reverses this strategy by showing the utility of epistemological insights and techniques for providing invariance conditions capable of regulating the applicability of the pure principles of choice. (shrink)

Heuristics can be regarded as justifying the actions and beliefs of problem-solving agents. I use an analysis of heuristics to argue that a symbiotic relationship exists between traditional epistemology and contemporary artificial intelligence. On one hand, the study of models of problem-solving agents usingquantitative heuristics, for example computer programs, can reveal insight into the understanding of human patterns of epistemic justification by evaluating these models'' performance against human problem-solving. On the other hand,qualitative heuristics embody the justifying ability of defeasible rules, (...) the understanding of which is provided by traditional epistemology. (shrink)

The general conditions of epistemic defeat are naturally represented through the interplay of two distinct kinds of entailment, deductive and defeasible. Many of the current approaches to modeling defeasible reasoning seek to define defeasible entailment via model-theoretic notions like truth and satisfiability, which, I argue, fails to capture this fundamental distinction between truthpreserving and justification-preserving entailments. I present an alternative account of defeasible entailment and show how logic programming offers a paradigm in which the distinction can be captured, allowing for (...) the modeling of a larger range of types of defeat. This is possible through a natural extension of the declarative and procedural semantics of Horn clauses. (shrink)

We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We (...) prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive “flavor.” The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper. (shrink)

Most solutions to the sorites reject its major premise, i.e. the quantified conditional . This rejection appears to imply a discrimination between two elements that are supposed to be indiscriminable. Thus, the puzzle of the sorites involves in a fundamental way the notion of indiscriminability. This paper analyzes this relation and formalizes it, in a way that makes the rejection of the major premise more palatable. The intuitive idea is that we consider two elements indiscriminable by default, i.e. unless we (...) know some information that discriminates between them. Specifically, following Rough Set Theory, two elements are defined to be indiscernible if they agree on the vague property in question. Then, a is defined to be indiscriminable from b if a is indiscernible by default from b . That is to say, a is indiscriminable from b if it is consistent to assume that a and b agree on the relevant vague property. (shrink)

Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This (...) approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we replace the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories. (shrink)

We generalize Ripley’s results on the transitivity of consequence relation, without assuming a logic to be monotonic. Following Gabbay, we assume nonmonotonic consequence relation to be inclusive and cautious monotonic, and figure out the implications between different forms of transitivity of logical consequence. Weaker frameworks without inclusiveness or cautious monotonicity are also discussed. The paper may provide basis for the study of both non-transitive logics and nonmonotonic ones.

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)