A conjunction in closure spaces

This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see [6]). We shall prove many properties of ω-conjunctive closure spaces (X is ω-conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:

1. For every closed and proper subset of an ω-conjunctive closure space its interior is empty (i.e. it is a boundary set).
2. If X is an ω-conjunctive closure space which satisfies the ω-compactness theorem and \(\hat P\) [X] is a meet-distributive semilattice (see [3]), then the lattice of all closed subsets in X is a Heyting lattice.
3. A closure space is linear iff it is an ω-conjunctive and topological space.
4. Every continuous function preserves all conjunctions.

     

On Extracting Variable Herbrand Disjunctions

Studia Logica - Some quantitative results obtained by proof mining take the form of Herbrand disjunctions that may depend on additional parameters. We attempt to elucidate this fact through an...     

The Analytic Truth and Falsity of Disjunctions

Disjunctive inferences are difficult. According to the theory of mental models, it is because of the alternative possibilities to which disjunctions refer. Three experiments corroborated further predictions of the mental model theory. Participants judged that disjunctions, such as Either this year is a leap year or it is a common year are true. Given a disjunction such as Either A or B, they tended to evaluate the four cases in its ‘partition’: A and B, A and not‐B, not‐A and B, not‐A and not‐B, as ‘possible’ or ‘impossible’ in ways that bore out the difference between inclusive disjunctions (‘or both’) and exclusive disjunctions (‘but not both’). Knowledge usually concerns what is true, and so when participants judge that a disjunction is false, or contingent, and evaluate the cases in its partition, they depend on inferences that yield predictable errors. They tended to judge that disjunctions, such as follows: Either the food is cold or else it is tepid, but not both, are true, though in fact they could be false. They tended to infer ‘mirror‐image’ evaluations that yield the same possibilities for false disjunctions as those for true disjunctions. The article considers the implications of these results for alternative theories based on classical logic or on the probability calculus.     

Conjunctions,Disjunctions and Lewisian Semantics for Counterfactuals

Consider the reasonable axioms of subjunctive conditionals (1) if p q ₁ and p q ₂ at some world, then p (q ₁ & q ₂) at that world, and (2) if p ₁ q and p ₂ q at some world, then (p ₁ ∨ p ₂) q at that world, where p q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably false. I will then show how Lewisian semantics can be modified so as to assure (1) and (2) even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then.     

Responses to the Stigmatized: Disjunctions in Affect, Cognitions, and Behavior

This study examined affective, cognitive, and behavioral responses to members of a stigmatized group – homosexual men. Male participants were placed in a situation in which they anticipated interacting with a gray or a non-stigmatized conversation partner. The topic of the impending conversation was either potentially threatening or non-threatening. Participants in the gay conversation partner condition sat either farther away from the conversation partner (in the threat condition) or closer to the conversation partner (in the no-threat condition) than they did from non-stigmatized conversation partners. There were no differences in attitudes toward the conversation partner as a function of experimental condition. The results were interpreted in terms of predictions based on ambivalence-amplification theory, aversive racism theory, and the integrated threat theory.     

Conjunctions and/or Disjunctions： Radical Empiricism in the History of Philosophy

William James challenged the traditions of British Empiricism （Hume） on one hand and German Idealism （Kant and Hegel） on the other. James＇ ＂Radical Empiricism＂ is a via media （＂middle road＂） between these divergent positions. His central points of contention are the ontological status of relationships and the correct analysis of experience. British Empiricism leaves us with a world of separate, particular facts, based on atomic sense impressions. Idealists, on the other hand, claim that all worldly phenomena are conjoined by one rational principle. According to James＇ account, neither side recognizes that both conjunctive and disjunctive relations are integral to experience. Furthermore, James＇ critique proved to influence A. N. Whitehead＇s philosophy of experience and orientation toward Hume and Kant. This essay situates James＇ philosophy in this polemical and historical context.     

Processing inferences at the semantics/pragmatics frontier: Disjunctions and free choice

Linguistic inferences have traditionally been studied and categorized in several categories, such as entailments, implicatures or presuppositions. This typology is mostly based on traditional linguistic means, such as introspective judgments about phrases occurring in different constructions, in different conversational contexts. More recently, the processing properties of these inferences have also been studied (see, e.g., recent work showing that scalar implicatures is a costly phenomenon). Our focus is on free choice permission, a phenomenon by which conjunctive inferences are unexpectedly added to disjunctive sentences. For instance, a sentence such as “Mary is allowed to eat an ice-cream or a cake” is normally understood as granting permission both for eating an ice-cream and for eating a cake. We provide data from four processing studies, which show that, contrary to arguments coming from the theoretical literature, free choice inferences are different from scalar implicatures.     

对相容和不相容析取关系下析取句与条件句之间推理的比较

研究析取句和条件句之间的推理能检验推理心理学中的主要理论解释。一个实验考察了析取句和条件句中两个基本成分之间的关系(相容析取与不相容析取)和推理方向(由析取句推条件句与由条件句推析取句)对析取句与其等值的条件句之间推理的影响。结果发现,推理方向的影响取决于条件句和析取句中基本成分间的关系,在不相容析取关系下的推理成绩好于在相容析取关系下的推理成绩。现有的推理理论不能解释被试的整体反应模式,作者提出的特殊知识启发式与一般的句法意义对比启发式的竞争能统一解释被试的主导反应模式。     

Towards closure on closure

Tracking theories of knowledge are widely known to have the consequence that knowledge is not closed. Recent arguments by Vogel and Hawthorne claim both that there are no legitimate examples of knowledge without closure and that the costs of theories that deny closure are too great. This paper considers the tracking theories of Dretske and Nozick and the arguments by Vogel and Hawthorne. We reject the arguments of Vogel and Hawthorne and evaluate the costs of closure denial for tracking theories of knowledge.     

Getting a little closure for closure

Synthese - In this paper, I’ll survey a number of closure principles of epistemic justification and find them all wanting. However, it’ll be my contention that there’s a novel...     

Narrative closure

In this article, “Narrative Closure,” a theory of the nature of narrative closure is developed. Narrative closure is identified as the phenomenological feeling of finality that is generated when all the questions saliently posed by the narrative are answered. The article also includes a discussion of the intelligibility of attributing questions to narratives as well as a discussion of the mechanisms that achieve this. The article concludes by addressing certain recent criticisms of the view of narrative expounded by this article.     

Semantics in Banach spaces

A new approach to semantics, based on ordered Banach spaces, is proposed. The Banach spaces semantics arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and “fuzzy extensions” of Boolean as well as of non-Boolean semantics.     

Deductive closure

This is a brief review of issues over which Henry Kyburg and I differed concerning the requirement that full beliefs should be closed under deductive consequence.     

Semantic closure

This paper argues for tlie claims that a) a natural language such as English is semanticaly closed b) semantic closure implies inconsistency. A corollary of these is that the semantics of English must be paraconsistent. The first part of the paper formulates a definition of semantic closure which applies to natural languages and shows that this implies inconsistency. The second section argues that English is semeantically closed. The preceding discussion is predicated on the assumption that there are no truth value gaps. The next section of the paper considers whether the possibility of these makes any difference to the substantive conclusions of the previous sections, and argues that it does not. The crux of the preceding arguments is that none of the consistent semantical accounts that have been offered for solving the semantical paradoxes is a semantic ofEnglish. The final section of the paper produces a general argument as to why this must always be the case.     

Cellular spaces

This paper is an introduction into the theory of cellular spaces. From the more general model of nets of abstract cells which are interpreted by finite automata, it is shown how the model of cellular spaces is achieved by specialization. Cellular spaces are extremely homogeneous in function and in geometry. The relation between local and global behavior is regarded as the main topic of the theory. After a formal definition of cellular spaces, it is shown that not all functions of the configuration space are induced by cellular spaces. In addition, the Garden-of-Eden problem is discussed, and a simple self-reproduction property is explained.     

Psychodiagnosis in hypothetical problem spaces

Computer uses are demonstrated for designing a hypothetical psychodiagnostic system that can function in artificially created mental health environments. The idea is to simulate both a psychodiagnostic system and a clinician’s strategies in order to learn about computer as well as human information processing. An inductive method for teaching humans the elements of the diagnostic system and its solutions is also introduced.