Conditionals,Context, and the Suppression Effect

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B (e.g., from If it rained, Alicia got wet and It rained to Alicia got wet). Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise (e.g., If she forgot her umbrella, Alicia got wet) can lower participants’ rate of agreement—an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative conditional as a context‐sensitive strict conditional: true if and only if its consequent is true in each of a contextually determined set of situations in which its antecedent is true. Pragmatically, the theory claims that context changes in response to new assertions, including new conditional premises. Thus, the conclusion of a modus ponens argument may no longer be accepted in the changed context. Psychologically, the theory describes people as capable of reasoning about broad classes of possible situations, ordered by typicality, without having to reason about individual possible worlds. The theory accounts for the main suppression phenomena, and it generates some novel predictions that new experiments confirm.     

AI &; Law,Logic and Argument Schemes

This paper reviews the history of AI & Law research from the perspective of argument schemes. It starts with the observation that logic, although very well applicable to legal reasoning when there is uncertainty, vagueness and disagreement, is too abstract to give a fully satisfactory classification of legal argument types. It therefore needs to be supplemented with an argument-scheme approach, which classifies arguments not according to their logical form but according to their content, in particular, according to the roles that the various elements of an argument can play. This approach is then applied to legal reasoning, to identify some of the main legal argument schemes. It is also argued that much AI & Law research in fact employs the argument-scheme approach, although it usually is not presented as such. Finally, it is argued that the argument-scheme approach and the way it has been employed in AI & Law respects some of the main lessons to be learnt from Toulmin’s The Uses of Argument.     

充分条件句语义关系知觉对条件推理的影响

作者通过实验考察了大学生被试对五种充分条件句语义关系知觉对其条件推理的影响。两个实验的结果表明,被试对条件句中前后件之间语义关系的知觉理解影响和调节其相应的条件推理的成绩。实验1新发现,被试对充分条件句后件对前件必要性的知觉理解存在难易差异,对许可句和定义句的后件必要性容易知觉,对偶然句、义务句和因果句的后件必要性难以知觉。实验2新发现,被试对充分条件句后件对前件必要性的知觉理解的难易差异导致被试在否定后件式推理成绩上的差异,对许可句和定义句的否定后件式推理成绩显著高于对偶然句、义务句和因果句的否定后件式推理成绩,对充分条件句否定后件式推理成绩随对后件必要性知觉增加而增加。     

Ceteris Paribus Conditionals and Comparative Normalcy

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species of variably strict conditional I hope to shed new light upon their content and their logic.     

Some Embedding Theorems for Conditional Logic

We prove some embedding theorems for classical conditional logic, covering ‘finitely cumulative’ logics, ‘preferential’ logics and what we call ‘semi-monotonic’ logics. Technical tools called ‘partial frames’ and ‘frame morphisms’ in the context of neighborhood semantics are used in the proof.     

A Note on Binary Inductive Logic

We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.     

条件推理的语义关系表达形式效应

作者用以大学生为被试的实验考察, 基本条件句语义关系表达形式(充分关系、必要关系和析取关系表达形式)和作为心理模型外显建构的可能性判断任务对条件推理的可能影响。实验结果发现, 条件推理的语义关系表达形式效应显著, 条件句语义关系表达形式对被试条件推理有显著的影响, 条件推理成绩随条件句语义关系表达的外显程度增加而增加; 被试在可能性判断任务中对条件句所含心理模型的外显建构并没有明显改善条件推理的成绩; 在有可能性判断任务条件下, 被试外显心理模型建构的成绩变化模式并不能一致地预测条件推理成绩的变化模式。这些结果说明, 人们的条件推理可能并不是完全基于心理模型建构, 而是还受对条件句前后件之间语义关系理解的影响; 条件句表达形式中语义关系的外显内隐模式影响对条件句语义关系的知觉理解难易, 从而影响相应条件推理的成绩。     

Kaufmann on the Probabilities of Conditionals

Kaufmann has recently argued that the thesis according to which the probability of an indicative conditional equals the conditional probability of the consequent given the antecedent under certain specifiable circumstances deviates from intuition. He presents a method for calculating the probability of a conditional that does seem to give the intuitively correct result under those circumstances. However, the present paper shows that Kaufmann’s method is inconsistent in that it may lead one to assign different probabilities to a single conditional at the same time.     

Logic programming,probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.     

Beyond Language: Using Logic to Introduce New Philosophical Distinctions

Philosophy has to be communicable in language, and therefore, whatever it has to say must be expressible in (some) language. But in order to make progress, philosophy has to gradually extend and improve its terminological apparatus. It is argued that logical formalization is a highly useful tool for discovering and confirming distinctions that are not present in ordinary language or in pre-existing philosophical terminology. In particular, it is proposed that if two usages of a word require different logical formalizations, then that is a strong reason to distinguish between them also in informal philosophy. The distinction between two types of normative conditionals, conditional veritable norms and conditional normative rules, is used as an example to corroborate this proposal.     

Conditionals and consequences

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.     

Nineteenth Century British Logic on Hypotheticals,Conditionals, and Implication

Hypotheticals, conditionals, and their connecting relation, implication, dramatically changed their meanings during the nineteenth and early part of the twentieth century. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different, their ties to the implication relation either were unclear, or the implication relation was used exclusively as a logical operator. I will trace the development of implication as an inference operator from these earlier notions into the first third of the twentieth century using as the starting point the ideas primarily of R. Whately and W. Hamilton before discussing the work of the transitional logicians, A. De Morgan and G. Boole on these topics. Then we discuss the relevant views of four prominent but relatively unknown nineteenth century British logicians, W.E. Johnson, J.N. Keynes, E.E.C. Jones, and H. MacColl, as well as those of the more influential logicians, W.S. Jevons and J. Venn, closing with a section on ‘implication as inference’ where we explore some key ideas of B. Russell and sketch the work of D. Hilbert, P. Hertz, and G. Gentzen who together are responsible for the development of the modern ideas related to the subjects of this paper.     

Martin's Axiom,Omitting Types,and Complete Representations in Algebraic Logic

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin's axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey's omitting types theorem fails for L _n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L _n has been recently (and quite extensively) studied as a many-dimensional modal logic.     

On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic

In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.     

The Mental Model Theory of Conditionals: A Reply to Guy Politzer

This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.     

The Suppression of Inferences From Counterfactual Conditionals

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, “if she watered the plants they bloomed,” when beliefs about additional background conditions, for example, “if the sun shone they bloomed” decrease the frequency of inferences such as modus tollens (from “the plants did not bloom” to “therefore she did not water them”). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, “if she had watered the plants they would have bloomed,” when beliefs about the known or presupposed facts, “she did not water the plants and they did not bloom” increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from “she did not water the plants” to “therefore they did not bloom”) is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new “switched-suppression” effect for conditionals with negated components, for example, “if she had not watered the plants they would not have bloomed”: modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning.