An erotetic approach to explanation by specification

In earlier publications of the first author it was shown that intentional explanation of actions, functional explanation of biological traits and causal explanation of abnormal events share a common structure. They are called explanation by specification (of a goal, a biological function, an abnormal causal factor, respectively) as opposed to explanation by subsumption under a law. Explanation by specification is guided by a schematic train of thought, of which the argumentative steps not concerning questions were already shown to be logically valid (elementary) arguments.Independently, the second author developed a new, inferential approach to erotetic logic, the logic of questions. In this approach arguments resulting in questions, with declarative sentences and/or other questions as premises, are analyzed, and validity of such arguments is defined.In the present paper it is shown that all four kinds of erotetic argumentative steps occurring in the train of thought of explanation by specification are valid arguments in the sense of inferential erotetic logic. Hence, in view of the fact that the other argumentative steps were already shown to be valid, it may be concluded that the logical structure of explanation by specification can be as well-established as that of explanation by nomological subsumption. Moreover, explanation by specification provides some illustrations of the applicability of erotetic logic in everyday life and some empirical sciences.     

A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

In recent years, the effort to formalize erotetic inferences—i.e., inferences to and from questions—has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and erotetic implication. While an effort has been made to axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system.

     

Erotetic Logic And Explanation By Abnormic Hypotheses

A relativized concept of a possiblecorrect answer to a why-question is introduced. Acertain procedure of looking for acceptable answers towhy-questions is analyzed in terms of erotetic logic,i.e., the logic of questions.     

Erotetic arguments: A preliminary analysis

The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.     

Deduction and Reduction Theorems for Inferential Erotetic Logic

The concepts of question evocation and erotetic implication play central role in Inferential Erotetic Logic. In this paper, deduction theorems for question evocation and erotetic implication are proven. Moreover, it is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set, and how erotetic implication based on a finite non-empty set of declaratives can be reduced to a relation between questions only.     

Illusory inferences with quantifiers

The psychological study of reasoning with quantifiers has predominantly focused on inference patterns studied by Aristotle about two millennia ago. Modern logic has shown a wealth of inference patterns involving quantifiers that are far beyond the expressive power of Aristotelian syllogisms, and whose psychology should be explored. We bring to light a novel class of fallacious inference patterns, some of which are so attractive that they are tantamount to cognitive illusions. In tandem with recent insights from linguistics that quantifiers like “some” are treated as wh-questions, these illusory inferences are predicted by the erotetic theory of reasoning, which postulates that a process akin to question asking and answering is behind human inference making.     

Emergence,Story, and the Challenge of Positive Scenarios

This article is divided into three parts. The first part describes the paradox of positive scenarios: they are much harder to write than negative scenarios. The second part describes the logic of emergent systems whose properties are neither reducible to nor predictable from the properties of their component parts. The third part shows how the concept of emergence can be used to lend plausibility to those optimistic scenarios that might otherwise be rejected as mere wishful thinking.     

Objectivity and a comparison of methodological scenario approaches for climate change research

Climate change assessments rely upon scenarios of socioeconomic developments to conceptualize alternative outcomes for global greenhouse gas emissions. These are used in conjunction with climate models to make projections of future climate. Specifically, the estimations of greenhouse gas emissions based on socioeconomic scenarios constrain climate models in their outcomes of temperatures, precipitation, etc. Traditionally, the fundamental logic of the socioeconomic scenarios—that is, the logic that makes them plausible—is developed and prioritized using methods that are very subjective. This introduces a fundamental challenge for climate change assessment: The veracity of projections of future climate currently rests on subjective ground. We elaborate on these subjective aspects of scenarios in climate change research. We then consider an alternative method for developing scenarios, a systems dynamics approach called ‘Cross-Impact Balance’ (CIB) analysis. We discuss notions of ‘objective’ and ‘objectivity’ as criteria for distinguishing appropriate scenario methods for climate change research. We distinguish seven distinct meanings of ‘objective,’ and demonstrate that CIB analysis is more objective than traditional subjective approaches. However, we also consider criticisms concerning which of the seven meanings of ‘objective’ are appropriate for scenario work. Finally, we arrive at conclusions regarding which meanings of ‘objective’ and ‘objectivity’ are relevant for climate change research. Because scientific assessments uncover knowledge relevant to the responses of a real, independently existing climate system, this requires scenario methodologies employed in such studies to also uphold the seven meanings of ‘objective’ and ‘objectivity.’     

Successful or unsuccessful search for risk defusing operators: Effects on decision behaviour

In experiments with quasi-realistic risky scenarios instead of gambles, decision makers are less interested in probability information. Often, they actively search for a risk defusing operator (RDO; an action to be performed in addition to a specific alternative and expected to decrease the risk involved). Examples in daily life are insurance and vaccination. In our experiment, the central independent variable was the successful or unsuccessful RDO search. The central dependent variables were choices and information search behaviour. In order to get information about the applied heuristics, a concurrent Thinking Aloud procedure was employed in addition to the method of Active Information Search. Eighty subjects made a choice in two risky scenarios. The findings confirm that the successful search for an RDO for one of the alternatives is an excellent predictor of choice. If the subject does not search for an RDO or the search is unsuccessful, MAXIMIN was the most frequent heuristic.     

Scientific problems and questions from a logical point of view

Scientific knowledge systems function as effective and specialized apparatus for formulating, analyzing and solving scientific problems. In science, problems become internal parts of the knowledge systems; thus they acquire new forms and properties in comparison with common-sense problems. Definite theoretical structures connected with problems and questions appear in the theory. Among them are erotetic expressions and languages, calculi and algebras of problems. On the basis of the structure-nominative reconstruction of a theory, the unified treatment of these structures is given. Methods of the theory of named sets are used in the logical analysis of problems and their systems. As a consequence a new formalized model of the problem part of theory is constructed.     

A relevance theory of induction

A framework theory, organized around the principle of relevance, is proposed for category-based reasoning. According to the relevance principle, people assume that premises are informative with respect to conclusions. This idea leads to the prediction that people will use causal scenarios and property reinforcement strategies in inductive reasoning. These predictions are contrasted with both existing models and normative logic. Judgments of argument strength were gathered in three different countries, and the results showed the importance of both causal scenarios and property reinforcement in categorybased inferences. The relation between the relevance framework and existing models of category-based inductive reasoning is discussed in the light of these findings.     

Getting satisfied with “satisfaction of search”: How to measure errors during multiple-target visual search

Visual search studies are common in cognitive psychology, and the results generally focus upon accuracy, response times, or both. Most research has focused upon search scenarios where no more than 1 target will be present for any single trial. However, if multiple targets can be present on a single trial, it introduces an additional source of error because the found target can interfere with subsequent search performance. These errors have been studied thoroughly in radiology for decades, although their emphasis in cognitive psychology studies has been more recent. One particular issue with multiple-target search is that these subsequent search errors (i.e., specific errors which occur following a found target) are measured differently by different studies. There is currently no guidance as to which measurement method is best or what impact different measurement methods could have upon various results and conclusions. The current investigation provides two efforts to address these issues. First, the existing literature is reviewed to clarify the appropriate scenarios where subsequent search errors could be observed. Second, several different measurement methods are used with several existing datasets to contrast and compare how each method would have affected the results and conclusions of those studies. The evidence is then used to provide appropriate guidelines for measuring multiple-target search errors in future studies.     

Automatic verification of multi-agent systems by model checking via ordered binary decision diagrams

We present a methodology for the verification of multi-agent systems, whose properties are specified by means of a modal logic that includes a temporal, an epistemic, and a modal operator to reason about correct behaviour of agents. The verification technique relies on model checking via ordered binary decision diagrams. We present an implementation and report on experimental results for two scenarios: the bit transmission problem with faults and the protocol of the dining cryptographers.     

Toward a Dynamic Logic of Questions

Questions are triggers for explicit events of ‘issue management’. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to multi-agent scenarios and long-term temporal protocols. We sketch a comparison with some alternative accounts.     

Stoic Sequent Logic and Proof Theory

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness.     

Husserl’s Foundation of the Formal Sciences in his “Logical Investigations”

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations. First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction.     

Nonmonotonic abductive inductive learning

Inductive Logic Programming (ILP) is concerned with the task of generalising sets of positive and negative examples with respect to background knowledge expressed as logic programs. Negation as Failure (NAF) is a key feature of logic programming which provides a means for nonmonotonic commonsense reasoning under incomplete information. But, so far, most ILP research has been aimed at Horn programs which exclude NAF, and has failed to exploit the full potential of normal programs that allow NAF. By contrast, Abductive Logic Programming (ALP), a related task concerned with explaining observations with respect to a prior theory, has been well studied and applied in the context of normal logic programs. This paper shows how ALP can be used to provide a semantics and proof procedure for nonmonotonic ILP that utilises practical methods of language and search bias to reduce the search space. This is done by lifting an existing method called Hybrid Abductive Inductive Learning (HAIL) from Horn clauses to normal logic programs. To demonstrate its potential benefits, the resulting system, called XHAIL, is applied to a process modelling case study involving a nonmonotonic temporal Event Calculus (EC).     

Culture and collective argumentation

What are the mechanisms underlying the reproduction and change of collective beliefs? The paper suggests that a productive and promising approach for dealing with this question can be found in ontogenetic and cross-cultural studies on ‘collective argumentations and belief systems’; this is illustrated with regard to moral beliefs: After a short discussion of the rationality/relativity issue in cultural anthropology some basic elements of a conceptual framework for the empirical study of collective argumentations are outlined. A few empirical case studies are summarized; the results deliver some empirical evidence to the assumption that as the ‘logic of collective argumentations’ develops in children and adolescent there will be different and increasingly more complex constraints on the kinds of basic moral beliefs that can be collectively accepted. Most importantly, as children approach adolescence they may have acquired a ‘logic of argumentation’ which makes possible a collectively valid distinction between the ‘is’ and the ‘ought’ of some disputed particular moral issue. A comparison with a land litigation among Trobriands (Papua New Guinea) shows that the ‘logic of argumentation’ and the corresponding basic moral beliefs of Trobriands very much resemble the ‘logic of argumentation’ and moral rationality standards of (German) adolescents.     

Executive working memory load does not compromise perceptual processing during visual search: Evidence from additive factors analysis

Executive working memory (WM) load reduces the efficiency of visual search, but the mechanisms by which this occurs are not fully known. In the present study, we assessed the effect of executive load on perceptual processing during search. Participants performed a serial oculomotor search task, looking for a circle target among gapped-circle distractors. The participants performed the task under high and low executive WM load, and the visual quality (Experiment 1) or discriminability of targets and distractors (Experiment 2) was manipulated across trials. By the logic of the additive factors method (Sternberg, 1969, 1998), if WM load compromises the quality of perceptual processing during visual search, manipulations of WM load and perceptual processing difficulty should produce nonadditive effects. Contrary to this prediction, the effects of WM load and perceptual difficulty were additive. The results imply that executive WM load does not degrade perceptual analysis during visual search.