The causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In 10.1515/jci-2017-0020, one of us introduced the inflation technique for formulating useful relaxations of the causal compatibility problem in terms of (...) linear programming. In this work, we develop a formal hierarchy of such causal compatibility relaxations. We prove that inflation is asymptotically tight, i.e., that the hierarchy converges to a zero-error test for causal compatibility. In this sense, the inflation technique fulfills a longstanding desideratum in the field of causal inference. We quantify the rate of convergence by showing that any distribution which passes the nth-order inflation test must be On−1/2$\begin{array}{} \displaystyle {O}{\left(n^{{{-}{1}}/{2}}\right)} \end{array}$-close in Euclidean norm to some distribution genuinely compatible with the given causal structure. Furthermore, we show that for many causal structures, the (unrelaxed) causal compatibility problem is faithfully formulated already by either the first or second order inflation test. (shrink)

In what sense, and to what extent, do rules of inference determine the meaning of logical constants? Motivated by the principle of charity, a natural constraint on the interpretation of logical constants is to make the rules of inference come out sound. But, as Carnap observed, although this constraint does rule out some non-standard interpretations, it does not rule them all out. This is known as Carnap’s problem. I suggest that a charitable interpretation of the logical constants should, as far (...) as possible, make the rules of inference both sound and complete, and I show how this idea can be brought to bear on a successful solution to Carnap’s problem in the case of classical propositional logic, as well as classical first-order logic. In fact, the solution generalizes to any logic whose rules of inference are sound and complete with respect to a bivalent semantics that is classical with respect to negation. (shrink)

Perceptual completion fills the gap for discrete perception to become continuous. Similarly, dynamic perceptual completion provides an experience of dynamic continuity. Our recent discovery of the ‘happening’ element of DPC completes the total experience for dynamism in the flow of time. However, a phenomenological explanation for these experiences is essential. The Snapshot Hypotheses especially the Dynamic Snapshot View provides the most comprehensive explanation. From that understanding the ‘two times’ problem can be addressed. The static time of spacetime cosmologies has been (...) irreconcilable with the dynamic FOT. Dismissing the FOT as an illusion is unsatisfactory. Therefore, we provide four hypotheses for the TTP.1) Since cosmological static time demands that all events are discrete, DPC elements for dynamism should likewise be expected to be discrete and accounted for by a snapshot phenomenology such as the DSV. 2) If temporality can be demonstrated to be similar to apparent motion by being a snapshot phenomenon and not demanding temporal extension it would confirm the DSV and permit reconciliation with static time. 3) If the ‘present moment’ is subjective as static time theories suggest, it should be possible experimentally for an observer to choose his own ‘present’ by moving to various points in the past with the aid of virtual reality. 4) If dynamism e.g. motion can be precluded without significant information loss or violating physics principles it is a cognitive add-on, thereby contradicting non-static time theories which suggest that time is ‘real.’ We confirm those hypotheses. (shrink)

In 1969, John McCarthy and Pat Hayes uncovered a problem that has haunted the field of artificial intelligence ever since--the frame problem. The problem arises when logic is used to describe the effects of actions and events. Put simply, it is the problem of representing what remains unchanged as a result of an action or event. Many researchers in artificial intelligence believe that its solution is vital to the realization of the field's goals. Solving the Frame Problem presents the various (...) approaches to the frame problem that have been proposed over the years. The author presents the material chronologically--as an unfolding story rather than as a body of theory to be learned by rote. There are lessons to be learned even from the dead ends researchers have pursued, for they deepen our understanding of the issues surrounding the frame problem. In the book's concluding chapters, the author offers his own work on event calculus, which he claims comes very close to a complete solution to the frame problem. Artificial Intelligence series. (shrink)

Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.

In lieu of an abstract, here is a brief excerpt of the content:Solving the Jigsaw PuzzlePeggy CadetIn my medical record, there is an enigmatic note. It was written as a consultation request from a pediatric endocrinologist to a plastic surgeon while I was hospitalized at age 13 (in the late 1960s) for mastectomy. The note reads:You have seen this unfortunate teenager with the feminizing testis [older name for androgen insensitivity] syndrome on several occasions in the past in reference to the (...) construction of a penis. Would appreciate your seeing him again to evaluate the problem. He is firmly fixed in the male gender role despite efforts on the part of his father to persuade him of the logic of a change.The surgeon’s response (also in my notes) was:The prospect of creating an acceptable penis in this patient seems to me very remote. There is nothing there except an enlarged clitoris. This could be mobilized and might project a few cm but cannot be made into a male organ of normal dimensions. The hair distribution and the perineum is also feminine which compounds the reconstruction problem.Since the decision has been made to go along with the male gender I suppose that mobilization of the penis–clitoris is reasonable. Urethral reconstruction will be possible only much later....I saw this note for the first time at age 21 but didn’t think it was particularly significant until many years later. At the time I had other, much more pressing concerns, as I had reached the conclusion by then that I had been mis–assigned as a boy and that the only way for me to have a reasonable and happy life would be for me to change to living as a girl. It was not a surprise that my doctors had been completely on the wrong track about my “gender”. I was also not about to bring this up with the endocrinologist, a person who had terrified me as a child and whom I still found a bit intimidating.I do remember the surgeon stopping by and examining me briefly without explaining who he was or why he was there. I had a somewhat longer, but equally uninformative (for me) visit from a child psychiatrist. The note requesting a consultation from the psychiatrist reads:Would you see while he is here recovering from his mastectomy? Since he began to show mammary growth 18 months ago his father has put him under considerable pressure to undergo another change in gender role. has resisted but he is quite depressed. We would appreciate any suggestions you may have.I actually have no recollection at all of anything like pressure from my father to change to living as a girl. What I actually experienced was more like 180 degrees away from that—the expectation that I should try to be more masculine. As I remember, my father was bothered by my having breasts and was the one who initiated the physician contacts that led to mastectomy. (My mother had died when I was five, leaving him to rear me as a single parent.)As my father recollected to me many years later, he had asked the pediatric endocrinologist to explain all of my treatment options and alternatives to me. I can only guess, but possibly the pediatric endocrinologist interpreted this as my father wanting me to change to living as a girl. As a young [End Page E1] adult, I got the impression that this particular doctor tended to mistake asking for information about possible treatments for requesting treatment. The idea of a patient gathering information and making informed decisions may not have figured prominently in his thinking. On the office visit when I was 21 and first mentioned to him that I might want to live as a girl, he told me that gender identity was “an unshakable conviction,” so perhaps his idea was that gender was just not something a person could make an ordinary decision about, weighing the pros and cons.My father knew—but at age 13 I didn’t—that the original decision for me to grow up as a boy had been made in a somewhat haphazard way. I had entered... (shrink)

In the context of office work, learning to handle an Enterprise Resource Planning system is important as implementation costs for such systems and associated expectations are high. However, these expectations are often not met because the users are not trained adequately. Electronic Performance Support Systems are designed to support employees’ ERP-related problem-solving and informal learning. EPSS are supposed to enhance employees’ performance and informal workplace learning through task-specific and granular help in task performance and problem-solving. However, there is little empirical (...) research on EPSS. Two survey studies addressed this research gap. In the first study, 301 people working in Human Resource -related positions and functions evaluated the learning potential of EPSS as well as potential advantages and obstacles concerning the implementation and use of EPSS. Though other measures are currently assessed as more important for learning, HR employees expect a strong increase in the significance of EPSS for employee learning. In the second study, 652 users of ERP software completed a questionnaire on characteristics of their daily work tasks, team characteristics, individual dispositions, their coping with ERP-related problems, and characteristics of EPSS. Findings indicate that the most frequently available and used approach when dealing with an ERP-related problem is consulting colleagues. Three EPSS types can be distinguished by their increasing integration into the user interface and their context-sensitivity. While external and extrinsic EPSS are available to many users, intrinsic EPSS are less common but are used intensively if available. EPSS availability is identified to be a strong positive predictor of frequency of EPSS use, while agreeableness as well as the task complexity and information-processing requirements show small negative effects. Moreover, more intensive ERP users use EPSS more frequently. In general, ERP users value, features such as context-sensitivity, an integration of the EPSS into the ERP system’s user interface, the option to save one’s own notes, and information displayed in an extra window. It is expected that EPSS will play an important role in workplace learning in the future, along with other measures. (shrink)

I examine the relationship between complete analysis and clarificatory analysis and explain why Wittgenstein thought he required both in his account of how to solve the problems of philosophy. I first describe Wittgenstein’s view of how philosophical confusions arise, by explaining how it is possible to misunderstand the logic of everyday language. I argue that any method of logical analysis in the Tractatus will inevitably be circular, but explain why this does not threaten the prospect of solving philosophical problems. I (...) distinguish between complete and clarificatory analysis and argue that Wittgenstein’s ‘strictly correct’ philosophical method is clarificatory analysis. Finally I discuss the relationship between the two forms of analysis and claim that, although, at the time of writing the Tractatus, Wittgenstein believed that the possibility of complete analysis underpins clarificatory analysis, in fact this was a mistake. In the Philosophical Investigations complete analysis is rejected and clarificatory analysis is retained. (shrink)

This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how (...) Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory. (shrink)

The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal the mathematically (...) exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity. (shrink)

Science and Community: Ending Obesity Improving Health (S&C) aimed to reduce obesity in Houston by developing community partnerships to identify research priorities and develop a sustainable obesity reduction program. Partnership members were recruited from S&C events and invited to participate in in‐depth interviews to gain insight into obesity prevalence, causes, and solutions. Members (n = 22) completed a 60–90‐min in‐depth interview. The interview guide consisted of 30 questions about pressing health problems in the community, potential solutions to health problems and (...) obesity and how the environment has impacted obesity and health behaviors in the community. Interviewees (n = 12 women and 10 men) were mostly Hispanic/Latino (n = 9) and African American (n = 7). Common problems identified were childhood obesity, balancing a healthy diet and physical inactivity. Interviewees identified obesity as a major problem in their communities and cited access to quality food and physical activity resources as both a problem and a solution. Additional emergent themes focused on solutions, including increasing awareness and education, coordinated efforts among organizations and using an ecologic approach to combat obesity. Community insight gleaned from this study may be used to enhance relevance and sustainability of programs developed to reduce obesity and suggests possible avenues for participatory research and intervention. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as (...) well. A solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

Artificial Intelligence as a discipline has gotten bogged down in subproblems of intelligence. These subproblems are the result of applying reductionist methods to the goal of creating a complete artificial thinking mind. In Brooks (1987) 1 have argued that these methods will lead us to solving irrelevant problems; interesting as intellectual puzzles, but useless in the long run for creating an artificial being.

We introduce the notion of “δ-complete decision procedures” for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of Lipschitz-continuous ODEs. Given an SMT problemϕ and a positive rational number δ, a δ-complete decision procedure determines either that ϕ is unsatisfiable, or that the “δ-weakening” of ϕ is satisfiable. Here, the δ-weakening of ϕ is a variant of ϕ that allows δ-bounded numerical perturbations on ϕ. We (...) establish the existence and complexity of δ-complete decision procedures for bounded SMT over reals with functions mentioned above. We propose to use δ-completeness as an ideal requirement for numerically-driven decision procedures. As a concrete example, we formally analyze the DPLL〈ICP〉 framework, which integrates Interval Constraint Propagation in DPLL, and establish necessary and sufficient conditions for its δ-completeness. We discuss practical applications of δ-complete decision procedures for correctness-critical applications including formal verification and theorem proving. (shrink)

Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of our success as species is that we, Homo sapiens, are the first and the only Turing complete species. Turing completeness is the capacity of some hardware to compute by software whatever hardware can compute. To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing is for (...) solving problems, and software is much cheaper than hardware, resulting that Turing completeness is evolutionarily disruptive. This conclusion, together with the fact that we are the only Turing complete species, is the reason that explains why we are so many. Most of our unique cognitive characteristics as humans can be derived from being Turing complete, as for example our complete language and our problem solving creativity. (shrink)

In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...) consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas. (shrink)

We provide a sound and complete proof system for an extension of Kleene’s ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of “is defined” is extended to terms and formulas via a straightforward recursive algorithm. The “is defined” formulas are constructed so that they themselves are always defined. The completeness proof relies on the Henkin construction. For each formula, precisely one of the (...) formula, its negation, and the negation of its “is defined” formula is true on the constructed model. Many other ternary logics in the literature can be reduced to ours. Partial functions are ubiquitous in computer science and even in (in)equation solving at schools. Our work was motivated by an attempt to precisely explain, in terms of logic, typical informal methods of reasoning in such applications. (shrink)

Recent work in the metaphysics of gender mostly focuses on trying to solve the exclusion problem - roughly, the problem of giving a metaphysical account of gender that doesn’t exclude anyone from their appropriate gender category. It is acknowledged that no completely satisfactory answer to the exclusion problem has yet been given in the literature; typically such theories fail to account for the diverse experiences and characteristics of trans people. One response is to adopt an anti-realism about gender properties, (...) such as Heather Logue’s gender fictionalism. I rebut the move to an anti-realism, showing that it relies on assuming a representationalism about gender vocabulary that we need not hold. I put forward a non-representationalist theory of gender properties that analyses gender vocabulary in terms of its inferential profile, rather than its representational features. This theory constitutes a deflationary realism about gender properties; it solves the inclusion problem, and guarantees the first-person epistemic authority of an individual regarding their own gender identity. (shrink)

In amodal completion the mind in some sense completes the visual perceptual representation of a scene by representing parts of the scene hidden behind other objects. Cognitive science has had a lot to say about how amodal completion occurs but has had little to say about the format of the representations involved and the way in which they represent. Some philosophers hold that amodal completions take the form of sensory imaginings of the occluded portions. This theory poses a puzzle for (...) both philosophy and neuroscience about how the occluded parts are imagined to be located relative to the unoccluded parts. A better theory begins with the observation that for many purposes it is useful to suppose that the mind contains mental models of three-dimensional structure. Visual perceptions and mental images may be conceived as mental models that represent external scenes by virtue of homomorphism and which possess both a deep aspect, representing both visible and occluded three-dimensional structure, and a perspectival aspect, representing only an arrangement of visible surfaces. In these terms we can explain various problem-solving abilities, such as the ability to imagine what a scene will look like from another point of view. Amodal completions can be treated as deep perceptual representations of three-dimensional structure. Thus amodal completions do not consist of mental imagery, but they can be used to generate mental imagery representing how a scene would look from alternative points of view. (shrink)

In a trio of recent articles, Johnson and Nado defend a form of metasemantic dispositionalism, arguing for a novel approach to the “error”-problem, based on speakers’ dispositional states under what they call a state of “full information”. In this article, I argue that their brand of dispositionalism fails to solve the “error”-problem, because of what I think of as counterexamples to it. In the final sections, I propose a way to amend the theory to shield it from some of the (...) counterexamples, based on the idea that what determines meaning is not only dispositions to apply words under full information, but also dispositions to evaluate one’s prior usage, under full information. (shrink)

I argue that the completeness of physics is composed of two distinct claims. The first is the commonly made claim that, roughly, every physical event is completely causally determined by physical events. The second has rarely, if ever, been explicitly stated in the literature and is the claim that microphysics provides a complete inventory of the fundamental categories that constitute both the causal features and intrinsic nature of all the events that causally affect the physical universe. After showing that (...) these claims are distinct, I argue that they can be used to solve a difficulty with existing responses to the exclusion problem—namely, that these existing responses also undermine the powerful causal argument for physicalism. Recognizing that there are two kinds of completeness opens up room for the nonreductive physicalist to solve the exclusion problem while also endorsing a modified, cogent causal argument for a kind of physicalism compatible with her position. (shrink)

Insight problem solving is thought to underpin creative thought as it incorporates both divergent (generating multiple ideas and solutions) and convergent (arriving at the optimal solution) thinking approaches. The current literature on schizotypy and creativity is mixed and requires clarification. An alternate approach was employed by designing an exploratory web-based study using only correlates of schizotypal traits (paranoia, dissociation, cognitive failures, fantasy proneness, and unusual sleep experiences) and examining which (if any) predicted optimal performance on an insight problem-solving task. One (...) hundred and twenty-one participants were recruited online from the general population and completed the number reduction task. The discovery of the hidden rule (HR) was used as a measure of insight. Multivariate logistic regression analyses highlighted persecutory ideation to best predict the discovery of the HR (OR = 1.05; 95% CI 1.01–1.10, p = 0.017), with a one-point increase in persecutory ideas corresponding to the participant being 5% more likely to discover the HR. This result suggests that persecutory ideation, above other schizotypy correlates, may be involved in insight problem solving. (shrink)

In this journal (Studia Logica), D. Rizza [2010: 176] expounded a solution of what he called “the indiscernibility problem for ante rem structuralism”, which is the problem to make sense of the presence, in structures, of objects that are indiscernible yet distinct, by only appealing to what that structure provides. We argue that Rizza’s solution is circular and expound a different solution that not only solves the problem for completely extensive structures, treated by Rizza, but for nearly (but not) (...) all mathematical structures. (shrink)

The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added (...) to the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments. (shrink)

In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...) consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas. (shrink)

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: extending the representation to the process of setting the problem, relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is (...) completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution. Completing the physical representation shows that the number of computation steps required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution. (shrink)

This comment asks us to imagine that we have discovered a principle that completely matches our intuitions about the various actions that might be performed in all the different versions of the trolley problem. Would that constitute a solution to the problem of providing a plausible principle to cover these various cases? Not necessarily, since the principle might turn on distinctions that have no obvious moral significance, and we might be unable to provide the principle with a compelling and (...) plausible rationale. It argues that this might well be the situation we find ourselves in with regard to the book’s proposed solution to the trolley problem: even if the principle does match our intuitions in how it sorts the cases, it is difficult to see why the distinctions on which it turns should matter, and appearances to the contrary notwithstanding, this comment believes the book has not provided the principle with a plausible account or rationale. (shrink)

This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ, where x occurs only positively in γ, we obtain the flat modal fixpoint language by adding to the language of polymodal logic a connective γ for each γΓ. The term γ is meant to be interpreted as the least fixed point of the functional interpretation of the term γ. We consider the following (...) problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen–Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...) computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

That alcohol provides a benefit to creative processes has long been assumed by popular culture, but to date has not been tested. The current experiment tested the effects of moderate alcohol intoxication on a common creative problem solving task, the Remote Associates Test . Individuals were brought to a blood alcohol content of approximately .075, and, after reaching peak intoxication, completed a battery of RAT items. Intoxicated individuals solved more RAT items, in less time, and were more likely to (...) perceive their solutions as the result of a sudden insight. Results are interpreted from an attentional control perspective. (shrink)

In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo''s logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in.

Open Shop Scheduling Problem is one of the most important scheduling problems in the field of engineering and industry. This kind of problem includes m machines and n jobs, each job contains a certain number of operations, and each operation has a predetermined processing time on its corresponding machine. The order of processing of these operations affects the completion times of all jobs. Therefore, the purpose of OSSP is to achieve a proper order of processing of jobs using specified machines, (...) so that the completion time of all jobs is minimized. In this paper, the strengths and limitations of three methods are evaluated by comparing the results of solving the OSSP in large-scale and small-scale benchmarks. In this case, the minimized completion time and total tardiness are considered the objective functions of the adapted methods. To solve small-scale problems, we adapt a mathematical model called Multiobjective Mixed Linear Programming. To solve large-scale problems, two metaheuristic algorithms including Multiobjective Parallel Genetic Algorithm and Multiobjective Parallel Simulated Annealing are adapted. In experimental results, we randomly generated small-scale problems to compare MOMILP with the Genetic Algorithm and Simulate Annealing. To compare MOPSA and MOPGA with the state of the art and show their strengths and limitations, we use a standard large-scale benchmark. The simulation results of the proposed algorithms show that although the MOPSA algorithm is faster, the MOPGA algorithm is more efficient in achieving optimal solutions for large-scale problems compared with other methods. (shrink)

Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two‐dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics‐naíve students were administered kinematics problems and spatial visualization ability tests. In Study 2, 17 (8 high‐ and 9 low‐spatial ability) additional students completed think‐aloud protocols while they solved the kinematics problems. In Study 3, the eye movements of (...) fifteen (9 high‐ and 6 low‐spatial ability) students were recorded while the students solved kinematics problems. In contrast to high‐spatial students, most low‐spatial students did not combine two motion vectors, were unable to switch frames of reference, and tended to interpret graphs literally. The results of the study suggest an important relationship between spatial visualization ability and solving kinematics problems with multiple spatial parameters. (shrink)

This is a magazine article discussing the philosophy of mathematics and arguing for mathematical conventionalism, written for a non-academic audience. (As often happens with popular articles, the editors made some changes that I'm not completely happy with, e.g., the titled section headings and sub-title).

Nonreductive physicalists endorse the principle of mental causation, according to which some events have mental causes: Sid climbs the hill because he wants to. Nonreductive physicalists also endorse the principle of physical causal completeness, according to which physical events have sufficient physical causes: Sid climbs the hill because a complex neural process in his brain triggered his climbing. Critics typically level the causal exclusion problem against this nonreductive physicalist model, according to which the physical cause is a sufficient cause of (...) the behavioural effect, so the mental cause is excluded from causally influencing Sid’s behaviour. In this paper I demonstrate how numerous nonreductive physicalists have responded to the causal exclusion problem by weakening the principle of physical causal completeness in numerous ways. The result: either numerous nonreductive physicalist solutions fail on account of the fact that they do not satisfy a robustly defined principle of physical causal completeness, or there is an accelerating trend of solving the causal exclusion problem by suitably weakening the principle of physical causal completeness. (shrink)

Emotional processing and social problem-solving are important for mental well-being. For example, impaired emotional processing is linked with depression and psychosomatic problems. However, little is known about crosscultural differences in emotional processing and social problem-solving and whether these constructs are linked. This study examines whether emotional processing and social problem-solving differs between Western and Eastern European cultures. Participants completed questionnaires assessing both constructs. Emotional processing did not differ according to culture, but Polish participants reported more effective social problem-solving abilities than (...) British participants. Poorer emotional processing was also found to relate to poorer social problem-solving. Possible societal reasons for the findings and the implications of the findings for culture and clinical practice are discussed. (shrink)

The paper offers a solution to the generality problem for a reliabilist epistemology, by developing an “algorithm and parameters” scheme for type-individuating cognitive processes. Algorithms are detailed procedures for mapping inputs to outputs. Parameters are psychological variables that systematically affect processing. The relevant process type for a given token is given by the complete algorithmic characterization of the token, along with the values of all the causally relevant parameters. The typing that results is far removed from the typings of folk (...) psychology, and from much of the epistemology literature. But it is principled and empirically grounded, and shows good prospects for yielding the desired epistemological verdicts. The paper articulates and elaborates the theory, drawing out some of its consequences. Toward the end, the fleshed-out theory is applied to two important case studies: hallucination and cognitive penetration of perception. (shrink)

This paper aims to solve a potential problem for the methodology of constitutive inference offered by Harbecke. The methodology is ultimately based on Mill’s “method of difference”, which requires a complete variation of factors in a given frame. In constitutive contexts, such a complete variation is often impossible. The offered solution utilizes the notion of a “mechanism slice”. In a first step, an example of a currently accepted explanation in neuroscience is reconstructed, which serves as a reference point of the (...) subsequent discussion. The regularity theory of mechanistic constitution and the corresponding methodology of constitutive inference are then introduced. Eventually, it is argued that the proposed solution accommodates well all schematic situations in which the impossibility of varying all test factors could be expected either to lead to false inferences or to preclude the establishment of correct constitutive claims. (shrink)

The quantification theory of propositions in Russell’s Principles of Mathematics has been the subject of an intensive study and in reconstruction has been found to be complete with respect to analogs of the truths of modern quantification theory. A difficulty arises in the reconstruction, however, because it presents universally quantified exportations of five of Russell’s axioms. This paper investigates whether a formal system can be found that is more faithful to Russell’s original prose. Russell offers axioms that are universally quantified (...) implications that have antecedent clauses that are conjunctions. The presence of conjunctions as antecedent clauses seems to doom the theory from the onset, it will be found that there is no way to prove conjunctions so that, after universal instantiation, one can detach the needed antecedent clauses. Amalgamating two of Russell’s axioms, this paper overcomes the difficulty. (shrink)

The study of insight in problem solving and creative thinking has seen an upsurge of interest in the last 30 years. Current theorising concerning insight has taken one of two tacks. The special-process view, which grew out of the Gestalt psychologists’ theorising about insight, proposes that insight is the result of a dedicated set of processes that is activated by the individual's reaching impasse while trying to deal with a problematic situation. In contrast, the business-as-usual view argues that insight is (...) brought about by the same processes that underlie ordinary thinking . Although those two views are typically treated as being in opposition, it has recently been proposed that a complete understanding of insight will require bringing together aspects of both views. The present paper carries that proposal further. Critical analysis of those two viewpoints demonstrates that each has a positive contribution to make to our understanding of insight, but also is.. (shrink)

In this paper, we bring together research on complex problem solving with that on motivational psychology about goal setting. Complex problems require motivational effort because of their inherent difficulties. Goal Setting Theory has shown with simple tasks that high, specific performance goals lead to better performance outcome than do-your-best goals. However, in complex tasks, learning goals have proven more effective than performance goals. Based on the Zurich Resource Model, so-called motto-goals should activate a person’s resources through positive affect. It was (...) found that motto-goals are effective with unpleasant duties. Therefore, we tested the hypothesis that motto-goals outperform learning and performance goals in the case of complex problems. A total of N = 123 subject participated in the experiment. In dependence of their goal condition, subjects developed a personal motto, learning, or performance goal. This goal was adapted for the computer-simulated complex scenario Tailorshop, where subjects worked as managers in a small fictional company. Other than expected, there was no main effect of goal condition for the management performance. An unexpected gender effect revealed better performance for men than women, pointing to a potential stereotype threat. As hypothesized, motto goals led to higher positive and lower negative affect than the other two goal types. Even though positive affect decreased and negative affect increased in all three groups during Tailorshop completion, participants with motto goals reported the lowest rates of negative affect. Exploratory analyses investigated the role of affect in complex problem solving via mediational analyses and the influence of goal type on perceived goal attainment. (shrink)

Naive deductivist accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H·X, for any X—even if X is completely irrelevant to E and H. Bayesian accounts of confirmation may appear to have the same problem. In a recent article in this journal Fitelson (2002) argued that existing Bayesian attempts to resolve of this problem are inadequate in several important respects. Fitelson then proposes a new‐and‐improved Bayesian account that overcomes the problem (...) of irrelevant conjunction, and does so in a more general setting than past attempts. We will show how to simplify and improve upon Fitelson's solution. (shrink)

This paper explores the effect of different types of incubation task (visual, numerical and verbal) with various levels of attentional focus and cognitive effort (non-demanding, low-demanding and high-demanding) on the resolution of insight problems. The most effective was found to be the low-demanding task (regardless of its nature), which although requiring attentional focus, leaves resources available for the unconscious analytical restructuring process, obtaining a high percentage of success in solving the problem shortly after completion of the incubation task. Overall findings (...) support the hypothesis of Unconscious Analytic Thought (UAT), according to which the restructuring required in insight problem solving implies a covert thinking process that includes a relevant, analytic and goal-oriented search. The findings are discussed in the light of UAT and are compared with the main theories of insight in problem solving. (shrink)

In United States v. Hensley, a unanimous Court set forth the rule that, "if police have a reasonable suspicion, grounded in specific and articulable facts, that a person they encounter was involved in or is wanted in connection with a completed felony, then a Terry stop may be made to investigate that suspicion." By expanding the scope of the Terry doctrine, Hensley strengthened the power of law enforcement officials to "stop and frisk" individuals who they believe may pose a threat (...) to the themselves and/or the public. Prior to Hensley, the Court's decisions merely sanctioned Terry stops of individuals that law enforcement officers reasonably suspected were about to commit a crime, or were committing a crime at the time of the stop. Thus, by authorizing Terry stops based on an officer's reasonable suspicion that an individual was involved in an already-completed felony, Hensley extended the types of situations under which law enforcement officers may engage in Terry stops. While explicitly expanding the scope of Terry v. Ohio in the context of completed felonies, the Hensley decision left open one major issue-whether the balancing test set forth in Hensley applies to investigatory stops based on an officer's reasonable suspicion that an individual was involved in a completed misdemeanor. With no answer from the Court, lower federal and state courts have attempted to answer this question on their own; in doing so, they have diverged on the issue. Most recently, in United States v. Grigg, the Ninth Circuit expanded the scope of Hensley and applied its balancing approach to Terry stops for completed misdemeanors. This Note argues against the Ninth Circuit's approach and rather for a per se rule against Terry stops for completed misdemeanors. This Note proposes that, in light of the inherent differences between misdemeanors and felonies, Hensley's balancing test should not extend to completed misdemeanors. Furthermore, the use of Terry stops for completed misdemeanors does not further the government and public interest in crime prevention and solving past crimes to an extent great enough to outweigh the great intrusion on privacy rights that Terry stops cause. Additionally, a per se rule provides for efficiency and guidance to police enforcement on routine patrols. Under such an approach, it is easier for private citizens to comprehend and appreciate their rights and understand when those rights are being violated. (shrink)

When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of doubt, mediate interactions between procedural and conceptual knowledge. To test these hypotheses, in two studies (Ns = 64 and 138), university students solved fraction and decimal arithmetic problems (...) while thinking aloud; verbal protocols and written work were coded for overt uses of conceptual knowledge and displays of doubt. Consistent with the hypotheses, use of conceptual knowledge during calculation was not significantly positively associated with accuracy, but was positively associated with displays of doubt, which were negatively associated with accuracy. In Study 1, participants also explained solutions to rational arithmetic problems; using conceptual knowledge in this context was positively correlated with calculation accuracy, but only among participants who did not use conceptual knowledge during calculation, suggesting that the correlation did not reflect “online” effects of using conceptual knowledge. In Study 2, participants also completed a nonroutine problem‐solving task; displays of doubt on this task were positively associated with accuracy, suggesting that metacognitive processes play different roles when solving routine and nonroutine problems. We discuss implications of the results regarding interactions between procedural knowledge, conceptual knowledge, and metacognitive processes in math problem solving. (shrink)

Insight problem solving is hindered by automated verbal–conceptual processes. Because mindfulness meditation training aims at “nonconceptual awareness” which involves a reduced influence of habitual verbal–conceptual processes on the interpretation of ongoing experience, mindfulness may facilitate insight problem solving. This hypothesis was examined across two studies . Participants in both studies completed a measure of trait mindfulness and a series of insight and noninsight problems. Further, participants in Study 2 completed measures of positive affect and a mindfulness or control training. The (...) results indicated that trait mindfulness predicts better insight but not noninsight problem solving , this relation is maintained when controlling for positive affect , mindfulness training improves insight but not noninsight problem solving and this improvement is partially mediated by state mindfulness . These findings are the first to document a direct relation between mindfulness and creativity. (shrink)

The most important property, a distinctive feature of any intelligent system, is its decision-making ability. In this case, the more complex the problem to be solved, the more and more diverse the initial data, and the more critical it is that the decision to be made was comprehensively considered and evaluated. In many cases, simultaneously arriving various initial data, if considered separately, and decisions based on such consideration lead to completely different results, often contradicting each other. Therefore, in (...) the process of development and implementation of artificial intelligence (AI), it is especially important to investigate the “mechanism” of decision-making in conditions of the inconsistency of incoming initial data and the need to establish some generalizing rule, according to which it is possible to find a harmonizing solution taking into account various influencing factors. It is evident that when establishing the rules of decision-making, it is necessary to strive for a “positive” result from the point of view of the problem being solved. This undoubtedly requires analyzing the consequences of the decision made in a set time scale, which can be provided by appropriate feedback that will allow us to make the necessary corrective actions. Artificial intelligence in modern forms of practical realization has, as a rule, a digital embodiment. It should be taken into account that the digital representation of data inevitably shows an inaccurate display of initial values when processes of a continuous nature are considered and analyzed. Since a digital model has certain limitations and characteristic properties when analyzing and processing initial data, it is logical to assume that for this reason, there can be some general approach, some general rule, according to which a decision is made in the conditions of diverse initial data and the need to take into account the relevant consequences after the decision is made. This paper attempts to find a decision-making mechanism, harmonizing it according to the incoming external and available internal input data. (shrink)