An unlabeled bracketing solution to the problem of conjoined phrases in Montague's PTQ

Conclusions Although Montague claims that the system of The proper treatment of quantification in ordinary English includes some conjunction and disjunction, the rules for other grammatical constructions do not take conjunction or disjunction into account, and in general fail either syntactically or semantically when one of their arguments is so formed. Using an unlabeled bracketing of syntactic structure and recursive definitions, we have been able to rewrite the rules so that correct results are obtained.These results should provide a firmer basis for extension of PTQ.This research was supported in part by NSF Grants GS-31309 and BNS 76-23840. Our observations were made with the aid of several computer programs for PTQ: a sentence generator for the bracketed syntax, a parser, and a translator. I should like to thank Philip Tedeschi, David Warren, and David Lewis for helpful discussions. Warren is also acknowledged as co-author of the section on the semantic role of conjunction.     

A developmental and cross-cultural study of the influences of rule structure and problem composition on the learning of conceptual classifications

Five experiments were conducted permitting direct comparisons in the way Ss of different ages and cultures solved conceptual problems. One group of problems (Traditional) could be solved using a reference rule of conjunction or disjunction. Another group of problems (Intradimensional) could be solved either by one of the reference rules, or by a structurally simpler rule. Analysis of American performance confirmed that older Ss not only solved using the simpler rule more often than younger Ss, but when they did so they solved faster. For both American age groups, solution using the simpler rule led to no difference in performance between conjunctive and disjunctive Intradimensional problems. Conjunction proved easier than disjunction only for the Traditional problems. Unlike Americans, the Kpelle of Liberia did not solve using the simpler rule, and found conjunction easier than disjunction for both Traditional and Intradimensional problems. When a memory aid was provided the Kpelle showed a pattern of performance exactly like Americans.     

Disjunction and conjunction fallacies in episodic memory

It has recently been found that episodic memory displays analogues of the well-known disjunction and conjunction fallacies of probability judgement. The aim of the present research was, for the first time, to study these memory fallacies together under the same conditions, and test theoretical predictions about the reasons for each. The focus was on predictions about the influence of semantic gist, target versus context recollection, and proactive versus retroactive interference. Disjunction and conjunction fallacies increased in conditions in which subjects were able to form semantic connections among list words. In addition, disjunction fallacies were increased by manipulations that minimised proactive interference, whereas conjunction fallacies were increased by manipulations that minimised retroactive interference. That pattern suggests that disjunction fallacies are more dependent on target recollection, whereas conjunction fallacies are more dependent on context recollection.     

The Relevance of a Relevantly Assertable Disjunction for Material Implication

In this paper Grice’s requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz’s conclusion-relevant consequence relation.     

The Compositionality of Logical Connectives in Child Italian

This paper investigates the interpretation that Italian-speaking children and adults assign to negative sentences with disjunction and negative sentences with conjunction. The aim of the study was to determine whether children and adults assign the same interpretation to these types of sentences. The Semantic Subset Principle (SSP) (Crain et al., in: Clifton, Frazer, Rayner (eds) Perspective on sentence processing, Lawrence Erlbaum, Hillside, 1994) predicts that children’s initial scope assignment should correspond to the interpretation that makes sentences true in the narrowest range of circumstances, even when this is not the interpretation assigned by adults. This prediction was borne out in previous studies in Japanese, Mandarin and Turkish. As predicted by the SSP, the findings of the present study indicate that Italian-speaking children and adults assign the same interpretation to negative sentences with conjunction (conjunction takes scope over negation). By contrast, the study revealed that some children differed from adults in the interpretation they assigned to negative sentences with disjunction. Adults interpreted disjunction as taking scope over negation, whereas children were divided into two groups: one group interpreted disjunction as taking scope over negation as adults did; another group interpreted negation as taking scope over disjunction, as predicted by the SSP. To explain the findings, we propose that Italian-speaking children initially differ from adults as dictated by the SSP, but children converge on the adult grammar earlier than children acquiring other languages due to the negative concord status of Italian, including the application of negative concord to sentences with disjunction.     

Fallacies in probability judgments for conjunctions and disjunctions of everyday events

The conjunction fallacy occurs when people judge a conjunction B‐and‐A as more probable than a constituent B, contrary to probability theory's ‘conjunction rule’ that a conjunction cannot be more probable than either constituent. Many studies have demonstrated this fallacy in people's reasoning about various experimental materials. Gigerenzer objects that from a ‘frequentist’ standpoint probability theory is not valid for these materials, and so failure to follow the conjunction rule is not a fallacy. This paper describes three experiments showing that the conjunction fallacy occurs as consistently for conjunctions where frequentist probability theory is valid (conjunctions of everyday weather events) as for other conjunctions. These experiments also demonstrate a reliable correlation between the occurrence of the conjunction fallacy and the disjunction fallacy (which arises when a disjunction B‐or‐A is judged less probable than a constituent B). This supports a probability theory + random variation account of probabilistic reasoning. Copyright © 2008 John Wiley & Sons, Ltd.     

An Analysis of Poly-connexivity

Studia Logica - Francez has suggested that connexivity can be predicated of connectives other than the conditional, in particular conjunction and disjunction. Since connexivity is not any...     

Acceptable Contradictions: Pragmatics or Semantics? A Reply to Cobreros et al.

Naive speakers find some logical contradictions acceptable, specifically borderline contradictions involving vague predicates such as Joe is and isn’t tall. In a recent paper, Cobreros et al. (J Philos Logic, 2012) suggest a pragmatic account of the acceptability of borderline contradictions. We show, however, that the pragmatic account predicts the wrong truth conditions for some examples with disjunction. As a remedy, we propose a semantic analysis instead. The analysis is close to a variant of fuzzy logic, but conjunction and disjunction are interpreted as intensional operators.     

The consistency of disjunctive assertions

In two experiments, we established a new phenomenon in reasoning from disjunctions of the grammatical form either A or else B, where A and B are clauses. When individuals have to assess whether pairs of assertions can be true at the same time, they tend to focus on the truth of each clause of an exclusive disjunction (and ignore the concurrent falsity of the other clause). Hence, they succumb to illusions of consistency and of inconsistency with pairs consisting of a disjunction and a conjunction (Experiment 1), and with simpler problems consisting of pairs of disjunctions, such as eIther there is a pie or else there is a cake and Either there isn't a pie or else there is a cake (Experiment 2), that appear to be consistent with one another, but in fact are not. These results corroborate the theory that reasoning depends on envisaging models of possibilities.     

Are conjunctive inferences easier than disjunctive inferences? A comparison of rules and models

We report four experiments investigating conjunctive inferences (from a conjunction and two conditional premises) and disjunctive inferences (from a disjunction and the same two conditionals). The mental model theory predicts that the conjunctive inferences, which require one model, should be easier than the disjunctive inferences, which require multiple models. Formal rule theories predict either the opposite result or no difference between the inferences. The experiments showed that the inferences were equally easy when the participants evaluated given conclusions, but that the conjunctive inferences were easier than the disjunctive inferences (1) when the participants drew their own conclusions, (2) when the conjunction and disjunction came last in the premises, (3) in the time the participants spent reading the premises and in responding to given conclusions, and (4) in their ratings of the difficulty of the inferences. The results support the model theory and demonstrate the importance of reasoners' inferential strategies.     

Propositional Plausible Logic: Introduction and Implementation

Plausible Logic allows defeasible deduction with arbitrary propositions, and yet when sufficiently simplified it is very similar to the Defeasible Logics of Billington and Nute. This paper presents Plausible Logic, explains some of the ideas behind the definitions, applies Plausible Logic to an example, and proves a coherence result which indicates that Plausible Logic is well behaved. We also report the first complete implementation of propositional Plausible Logic. The implementation has a web interface which makes it available to researchers and students everywhere. The implementation is evaluated experimentally, and is shown to be capable of handling tens of thousands of rules and sufficiently many disjunctions for realistic problems.     

A realist partner for Linda: confirming a theoretical hypothesis more than its observational sub-hypothesis

It is argued that the conjunction effect has a disjunctive analog of strong interest for the realism–antirealism debate. It is possible that a proper theory is more confirmed than its (more probable) observational sub-theory and hence than the latter’s disjunctive equivalent, i.e., the disjunction of all proper theories that are empirically equivalent to the given one. This is illustrated by a toy model.     

A Generalization of Inquisitive Semantics

This paper introduces a generalized version of inquisitive semantics, denoted as GIS, and concentrates especially on the role of disjunction in this general framework. Two alternative semantic conditions for disjunction are compared: the first one corresponds to the so-called tensor operator of dependence logic, and the second one is the standard condition for inquisitive disjunction. It is shown that GIS is intimately related to intuitionistic logic and its Kripke semantics. Using this framework, it is shown that the main results concerning inquisitive semantics, especially the axiomatization of inquisitive logic, can be viewed as particular cases of more general phenomena. In this connection, a class of non-standard superintuitionistic logics is introduced and studied. These logics share many interesting features with inquisitive logic, which is the strongest logic of this class.     

Quantum structure in cognition

The broader scope of our investigations is the search for the way in which concepts and their combinations carry and influence meaning and what this implies for human thought. More specifically, we examine the use of the mathematical formalism of quantum mechanics as a modeling instrument and propose a general mathematical modeling scheme for the combinations of concepts. We point out that quantum mechanical principles, such as superposition and interference, are at the origin of specific effects in cognition related to concept combinations, such as the guppy effect and the overextension and underextension of membership weights of items. We work out a concrete quantum mechanical model for a large set of experimental data of membership weights with overextension and underextension of items with respect to the conjunction and disjunction of pairs of concepts, and show that no classical model is possible for these data. We put forward an explanation by linking the presence of quantum aspects that model concept combinations to the basic process of concept formation. We investigate the implications of our quantum modeling scheme for the structure of human thought, and show the presence of a two-layer structure consisting of a classical logical layer and a quantum conceptual layer. We consider connections between our findings and phenomena such as the disjunction effect and the conjunction fallacy in decision theory, violations of the sure thing principle, and the Allais and Elsberg paradoxes in economics.     

Answer Sets and Qualitative Decision Making

Logic programs under answer set semantics have become popular as a knowledge representation formalism in Artificial Intelligence. In this paper we investigate the possibility of using answer sets for qualitative decision making. Our approach is based on an extension of the formalism, called logic programs with ordered disjunction (LPODs). These programs contain a new connective called ordered disjunction. The new connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means: if possible A, but if A is not possible then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show that LPODs can serve as a basis for qualitative decision making.     

Reasoning about complex probabilistic concepts in childhood

The competencies of children, particularly their understanding of the more complex probabilistic concepts, have not been thoroughly investigated. In the present study participants were required to choose the more likely of two events, a single event, and a joint event (conjunctive or disjunctive). It was predicted that the operation of the representativeness heuristic would result in erroneous judgements when children compared an unlikely component event with a likely-unlikely conjunction (the conjunction fallacy) and when a likely component event was compared to a likely-unlikely disjunction. The results supported the first prediction with both older children aged between 9 and 10 years and younger children aged between 4 and 5 committing the conjunction fallacy. However, the second prediction was not confirmed. It is proposed that the basis of representativeness judgements may differ between the conjunctive and disjunctive cases with absolute frequency information possibly playing a differential role.     

The Ambiguity of Quantifiers

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.     

Reflecting rules: A note on generalizing the deduction theorem

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all so-called ‘derivable rules’ can be encoded into the object language using the material conditional. The deduction theorem can be generalized in the sense that one can attempt to encode all types of rules into the object language. When a rule is encoded in this way I say that it is reflected in the object language. What I show, however, is that certain logics which reflect a certain kind of rule must be trivial. Therefore, my generalization of the deduction theorem does fail where the classic deduction theorem didn't.