A Theory of Conditionals

Stalnaker, Robert

doi:10.1007/978-94-009-9117-0_2

Cited by 1,273 publications

(847 citation statements)

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“…In outline, this idea resembles proposed methods for evaluating the truth value of counterfactual conditionals, such as if lions were 5 feet tall, then house cats would be 2 feet (see, e.g., Levi, 1996;Stalnaker, 1968). According to this method, you judge the counterfactual by revising your beliefs to accommodate the antecedent (lions are 5 feet tall).…”

Section: Discussionmentioning

confidence: 99%

Necessity and natural categories.

Rips

2001

Psychological Bulletin

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Our knowledge of natural categories includes beliefs not only about what is true of them but also about what would be true if the categories had properties other than (or in addition to) their actual ones. Evidence about these beliefs comes from three lines of research: experiments on category-based induction, on hypothetical transformations of category members, and on definitions of kind terms. The 1st part of this article examines results and theories arising from each of these research streams. The 2nd part considers possible unified theories for this domain, including theories based on ideals and norms. It also contrasts 2 broad frameworks for modal category information: one focusing on beliefs about intrinsic or essential properties, the other focusing on interacting causal relations.It's common ground in linguistics, artificial intelligence (AI), and philosophy that our knowledge of natural categories includes information that is resistant to exceptions. Linguists, for example, have described generic sentences, such as Lions have manes, as ones that are true, despite the existence of obvious and sometimes numerous exceptions (such as female lions and immature male lions; see Krifka et al., 1995). Likewise, research on nonmonotonic logic in AI has sought systems that can reason with such sentences without making mistakes or becoming inconsistent when exceptions arise (e.g., Ginsberg, 1987). Some theories in the philosophy of language invest everyday concepts such as lion with a status that allows them to play a role in counterfactual conditionals, such as If Calvin were a lion, he'd have a mane (e.g., Brandom, 1988Brandom, , 1994. Not only does our knowledge of categories withstand exceptional current circumstances, it stands as well in merely possible circumstances that we have not experienced.Cognitive psychology, however, has mostly treated beliefs about categories in terms of what's normal or usual rather than in terms of what's lawlike or exception resistant. Early theories of perceptual categorizing (e.g., Posner & Keele, 1968;Reed, 1972) emphasized the role of prototypes, consisting of average values of category members along their physical dimensions. According to these theories, if people have to classify, for example, schematic faces into two previously identified sets, they mentally compute a prototype for each set, where the prototype specifies the average values of the members of that set on dimensions such as width of mouth, length of nose, and distance between eyes. To decide which set a novel face belongs to, people then determine the distance between the new face and each of the category prototypes. Finally, people assign the new face to the set whose prototype is closest to this new item.National Science Foundation Grants SBR-9514491 and SES-9907414 supported this research. Thanks go to Serge Blok, Douglas Medin, Daniel Osherson, and Steven Sloman for comments on an earlier version of this article and to Beth Proffitt for conversations about the material in the first part of the article.Co...

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Section: Discussionmentioning

confidence: 99%

Necessity and natural categories.

Rips

2001

Psychological Bulletin

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“…In fact, according to Lewis [1971Lewis [ , 1973a and Stalnaker [1968], the above semantics does undergenerate. According to Lewis, the following should be valid:…”

Section: Counterfactualsmentioning

confidence: 99%

“…We will consider a semantics for the counterfactual language that is essentially due to Lewis [1971Lewis [ , 1973aLewis [ , 1973b and Stalnaker [1968] (also see Stalnaker and Thomason 1970). An ordering model for the counterfactual language consists of a set W of worlds, an assignment of subsets of W to proposition letters, and for each world w ∈ W , a reflexive and transitive binary relation w on W .…”

Section: Counterfactualsmentioning

confidence: 99%

Axiomatization in the Meaning Sciences

Holliday¹,

Icard²

2018

The Science of Meaning

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While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions-phenomena such as consistency and entailment-it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner.In this paper, we highlight some of the benefits of providing axiomatizations for the purpose of semantic theorizing. We illustrate some of these benefits using three examples from the study of modality.

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“…This is the syntax of conditional logic C2 of Stalnaker [119]. Models of C2 are of the form of a quadruple M = (W, R, S, E) where W is a set of possible worlds, R is an accessibility relation, S is a selector assigning to any formula α and any world w a world S(α, w) such that S(α, w) |= α and S(α, w) is closest to w and E assigns to any formula its extension i.e the set of worlds in which the formula is true.…”

Section: Conditional Logicsmentioning

confidence: 99%

Rough Sets and Rough Logic: A KDD Perspective

Pawlak

Polkowski

Skowron

2000

Rough Set Methods and Applications

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Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85,86] in the early 1980's. In the ensuing years, we have witnessed a systematic, world-wide growth of interest in rough sets and their applications.The main goal of rough set analysis is induction of approximations of concepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete. A fortiori, we have to describe concepts of interest (features, properties, relations etc.) not completely but by means of their reflections (i.e. approximations) in the chosen language. The most important issues in this induction process are:-construction of relevant primitive concepts from which approximations of more complex concepts are assembled, -measures of inclusion and similarity (closeness) on concepts, -construction of operations producing complex concepts from the primitive ones.Basic tools of rough set approach are related to concept approximations. They are defined by approximation spaces. For many applications, in particular for KDD problems, it is necessary to search for relevant approximation spaces in the large space of parameterized approximation spaces. Strategies for tuning parameters of approximation spaces are crucial for inducing concept approximations of high quality.Methods proposed in rough set approach are kin to general methods used to solve Knowledge Discovery and Data Mining (KDD) problems like feature selection, feature extraction (e.g. discretization or grouping of symbolic value),

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A Theory of Conditionals

Cited by 1,273 publications

References 5 publications

Necessity and natural categories.

Necessity and natural categories.

Axiomatization in the Meaning Sciences

Rough Sets and Rough Logic: A KDD Perspective

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