A Sequent Formulation of Conditional Logic Based on Belief Change Operations

Peter Gärdenfors has developed a semantics for conditional logic, based on the operations of expansion and revision applied to states of information. The account amounts to a formalisation of the Ramsey test for conditionals. A conditional A > B is declared accepted in a state of information K if B is accepted in the state of information which is the result of revising K with respect to A. While Gärdenfors's account takes the truth-functional part of the logic as given, the present paper proposes a semantics entirely based on epistemic states and operations on these states. The semantics is accompanied by a syntactic treatment of conditional logic which is formally similar to Gentzen's sequent formulation of natural deduction rules. Three of David Lewis's systems of conditional logic are represented. The formulations are attractive by virtue of their transparency and simplicity.     

Pretabular varieties of modal algebras

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras.     

Systematic Withdrawal

Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; Rott and Pagnucco, 1999). In this paper we present a new addition, systematic withdrawal, to the family of withdrawal operations, as they have become known. We define systematic withdrawal semantically, in terms of a set of preorders, and show that it can be characterised by a set of postulates. In a comparison of withdrawal operations we show that AGM contraction, systematic withdrawal and the severe withdrawal of Rott and Pagnucco (1999) are intimately connected by virtue of their definition in terms of sets of preorders. In a future paper it will be shown that this connection can be extended to include the epistemic entrenchment orderings of Gärdenfors (1988) and Gärdenfors and Makinson (1988) and the refined entrenchment orderings of Meyer et al. (2000).     

Merging without mystery or: Variables in dynamics semantics

In this paper we discuss the treatment of variables in dynamic semantics. Referent systems are introduced as a flexible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which we manipulate them — their names — and from the information that we store in them — their values. It is shown that the referent systems provide a natural basis for dynamic semantics. The semantics with referent systems is compared with the familiar formalisms in dynamic semantics,DRT andDPL.     

The systems approach — A. Bogdanov and L. von Bertalanffy

We undertake the comparison between Ludwig von Bertalanffy's General Systems Theory and Alexandr Bodganov's Tektology as two theories proposing a holistic interpretation of reality and claiming to solve problems which are unsolvable via conventional philosophic and scientific theories and methodologies. Basic misunderstandings by some Soviet authors regarding the nature of these theories — especially in the case of Tektology — are pointed out. The comparison is made in what concerns the general origins and purposes of the theories, their approaches to the problem of organization, their treatment of mathematics and their understanding of the cybernetic concept of regulation.We contend that Tektologycontains — some 15 years earlier — all the basic concepts which will be later developed by the General Theory of Systems. As we shall see, Tektology is the ultimate expansion of any theory of systems. This fact is widely ignored in contemporary specialized literature.We finally contend that both Tektology and the General Systems Theory are a sign of the times. A holistic secular monism is a respectable alternative to the failure of contemporary science and philosophy in guiding the life of men, in providing araison d'être for human existence. However, we do not explore the soundness of this alternative.     

Coherentist Contraction

A model of coherentist belief contraction is constructed. The outcome of belief contraction is required to be one of the coherent subsets of the original belief set, and a set of plausible properties is proposed for this set of coherent subsets. The contraction operators obtained in this way are shown to coincide with well-known belief base operations. This connection between coherentist and foundationalist approaches to belief change has important implications for the philosophical interpretation of models of belief change.     

Reversing the Levi identity

The AGM (Alchourrón-GÄrdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that arenot closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that onefirst adds the new belief to the belief base, and afterwards contracts its negation. It is argued that external revision represents an intuitively plausible way of revising one's beliefs. Since it typically involves the temporary acceptance of an inconsistent set of beliefs, it can only be used in belief representations that distinguish between different inconsistent sets of belief.     

Recovery Recovered

The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more closely to the identification of the beliefs contracted away in each counterexample case. Since, on our view, speakers" belief contraction intentions are often more complicated than they may first appear, we are led to develop apparatus for thinking about the communication and identification of those intentions. Our argument refocuses attention on the difficult question of how to apply the AGM theory to particular cases.     

Self-deception and belief attribution

One of the most common views about self-deception ascribes contradictory beliefs to the self-deceiver. In this paper it is argued that this view (the contradiction strategy) is inconsistent with plausible common-sense principles of belief attribution. Other dubious assumptions made by contradiction strategists are also examined. It is concluded that the contradiction strategy is an inadequate account of self-deception. Two other well-known views — those of Robert Audi and Alfred Mele — are investigated and found wanting. A new theory of self-deception relying on an extension of Mark Johnston's subintentional mental tropisms is proposed and defended.     

Contingent reliance on the affect heuristic as a function of regulatory focus

Results from four studies show that the reliance on affect as a heuristic of judgment and decision making is more pronounced under a promotion focus than under a prevention focus. Two different manifestations of this phenomenon were observed. Studies 1–3 show that different types of affective inputs are weighted more heavily under promotion than under prevention in person-impression formation, product evaluations, and social recommendations. Study 4 additionally shows that valuations performed under promotion are more scope-insensitive—a characteristic of affect-based valuations—than valuations performed under prevention. The greater reliance on affect as a heuristic under promotion seems to arise because promotion-focused individuals tend to find affective inputs more diagnostic, not because promotion increases the reliance on peripheral information per se.     

Multiple and iterated contraction reduced to single-step single-sentence contraction

Multiple contraction (simultaneous contraction by several sentences) and iterated contraction are investigated in the framework of specified meet contraction (s.m.c.) that is extended for this purpose. Multiple contraction is axiomatized, and so is finitely multiple contraction (contraction by a finite set of sentences). Two ways to reduce finitely multiple contraction to contraction by single sentences are introduced. The reduced operations are axiomatically characterized and their properties are investigated. Furthermore, it is shown how iterated contraction can be reduced to single-step, single-sentence contraction. However, in this framework the outcome of iterated contraction depends unavoidably on the order in which the inputs are received. This order-dependence makes it impossible to treat two inputs on an equal footing. Therefore it is often preferable to perform changes involving several pieces of information as multiple rather than iterated change.     

Basic Infobase Change

Generalisations of theory change involving arbitrary sets of wffs instead of belief sets have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation. In this paper we extend a proposal along these lines by Meyer et al. We take an infobase as a finite sequence of wffs, with each element in the sequence being seen as an independently obtained bit of information, and define appropriate infobase change operations. The associated theory change operations satisfy the AGM postulates for theory change. Since an infobase change operation produces a new infobase, it allows for iterated infobase change. We measure iterated infobase change against the postulates proposed by Darwiche et al. and Lehmann.     

Logical equations and admissible rules of inference with parameters in modal provability logics

This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman's problem forGL andS. We also show that A. V. Kuznetsov's problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions.     

The False Consensus Effect and Overconfidence: Flaws in Judgment or Flaws in How We Study Judgment?

Thefalse consensus effectand theoverconfidence in judgmenteffect are often referred to as established “facts” of psychology. At present, the empirical support for these effects is inadequate and logically flawed. We argue that, absent other information, using one's own response to a situation as an observation of size 1 could be an effective use of data and could lead to anincreasein the accuracy of predicting others’ behavior. In an empirical examination of such use, we find a robustpositivecorrelation between the degree to which people believe that a majority of others are like them and their accuracy in predicting those others’ responses, whether this correlation is evaluated within items across people, across items within people, or across items across people. In addition, we show that the finding of overconfidence in judgment follows analytically from the functional relationship used to demonstrate it, a “finding” that is easily reversed by considering the inverse relationship. Specifically, we argue that regression effects account for the evidence cited in support of overconfidence. While not definitive, our empirical findings call into the question the acceptance of these two effects—as commonly defined—as facts.     

Separating cue relevance from cue importance within models of judgment and decision making

Many investigations concerned with human decision making have centered their attention on the issues of cue integration and cue importance. Unfortunately, an equally important issue—that of cue relevance—has been either neglected or equated with the importance issue. Two experiments tested the ability of information integration theory (N. H. Anderson, 1981, Foundations of information integration theory, New York: Academic Press) to disentangle cue relevance and cue importance formally as well as empirically. The decision environment was divided into two components: aspects of the information present during a decision (information context) and aspects of the situation surrounding a decision (situation context). It was hypothesized that variations in information context would affect cue importance while changes in situation context would affect cue relevance. Furthermore, it was hypothesized that the weight parameter (w) of information integration theory would reflect the information context manipulations but not situation context manipulations. Results supported previous findings showing the influence of information context on w. As predicted situation context did not affect w; however, it did affect the variability of the responses to a cue's values. The relationship between perceived variability and situation context suggests that the scale dispersion parameter σ of information integration theory may be used as a measure of relevance (K. L. Norman, 1980, Organizational Behavior and Human Performance, 25, 289–310).     

Beliefs Don't Always Persevere: How Political Figures Are Punished When Positive Information about Them Is Discredited

Recent research has extended the belief‐perseverance paradigm to the political realm, showing that negative information about political figures has a persistent effect on political opinions even after it has been discredited. However, little is known about the effects of false positive information about political figures. In three experiments, we find that discrediting positive information generates a “punishment effect” that is inconsistent with the previous literature on belief perseverance. We argue people attempt to adjust for the perceived influence of the false claim when the information is discredited. In this case, when trying to account for the effects of discredited positive information about a politician, people overestimate how much correction is needed and thus end up with a more negative opinion. (By contrast, people underestimate how much correction is needed to adjust for false negative information, leading to belief perseverance.) These results suggest that bogus credit claiming or other positive misinformation can have severe repercussions for politicians.     

Reversal operations after brain damage

The ability to perform reversals—that is, the appreciation of the relationship between original and transformed states of knowledge—is critical to human thought processes. In order to assess whether a number of “special-purpose processors” are responsible for reversal operations, depending on the particular context in which the reversal is couched, or whether a single “core processing mechanism” subserves a critical aspect of reversal operations regardless of the specific context, patients with localized brain damage were asked to solve eight reversal problems. Visual and auditory reversals mediated by linguistic and non-linguistic symbol systems were presented. The findings demonstrate that patients with insult to the anterior portion of the right hemisphere encounter more difficulty performing reversals than patients with right posterior insult, Broca's aphasics, and fluent aphasics. This is regardless of the symbol system mediating the reversal, regardless of the modality of presentation, and regardless of the amount of available processing time. Subjects with insult to the posterior region of the left hemisphere or the right hemisphere also exhibit some difficulty solving reversal problems, although their difficulties appear modality specific. These data lend support to the claim that a core processing mechanism may play a critical role in the performance of reversal operations.     

Experimental test of the prospect theory value function: A stochastic dominance approach

According to prospect theory, individuals are risk averse regarding gains but risk seeking regarding losses, implying an S-shaped value function. The S-shaped value function hypothesis is based on experiments in which subjects are asked to choose separately between alternatives with either only positive or only negative outcomes, alternatives which rarely exist in the capital market. In addition, the S-shaped findings may be biased by the “certainty effect” and by probability distortion. In this paper we employ the recently developed prospect stochastic dominance criterion to test the prospect theory S-shaped value function hypothesis with mixed outcomes and with no “certainty effect.” Assuming that subjects do not distort moderate probabilities, we strongly reject the prospect theory S-shaped value function, with at least 76–86% of the choices being inconsistent with such preferences. When possible subjective probability distortions are taken into account, we find that at least 50–66% of the choices are inconsistent with an S-shaped value function.     

Many Concepts and Two Logics of Algorithmic Reduction

Within the program of finding axiomatizations for various parts of computability logic, it was proven earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting’s intuitionistic calculus. That sort of reduction permits unlimited reusage of the computational resource represented by the antecedent. An at least equally basic and natural sort of algorithmic reduction, however, is the one that does not allow such reusage. The present article shows that turning the logic of the first sort of reduction into the logic of the second sort of reduction takes nothing more than just deleting the contraction rule from its Gentzen-style axiomatization. The first (Turing) sort of interactive reduction is also shown to come in three natural versions. While those three versions are very different from each other, their logical behaviors (in isolation) turn out to be indistinguishable, with that common behavior being precisely captured by implicative intuitionistic logic. Among the other contributions of the present article is an informal introduction of a series of new — finite and bounded — versions of recurrence operations and the associated reduction operations. Presented by Robert Goldblatt