Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between [math] principles over [math]-models of [math]. They also introduced a version of this game that similarly captures provability over [math]. We generalize and extend this game-theoretic framework to other formal systems, and establish a certain compactness result that shows that if an implication [math] between two (...) principles holds, then there exists a winning strategy that achieves victory in a number of moves bounded by a number independent of the specific run of the game. This compactness result generalizes an old proof-theoretic fact noted by H. Wang (1981), and has applications to the reverse mathematics of combinatorial principles. We also demonstrate how this framework leads to a new kind of analysis of the logical strength of mathematical problems that refines both that of reverse mathematics and that of computability-theoretic notions such as Weihrauch reducibility, allowing for a kind of fine-structural comparison between [math] principles that has both computability-theoretic and proof-theoretic aspects, and can help us distinguish between these, for example by showing that a certain use of a principle in a proof is “purely proof-theoretic”, as opposed to relying on its computability-theoretic strength. We give examples of this analysis to a number of principles at the level of [math], uncovering new differences between their logical strengths. (shrink)

Talk of ‘robustness’ remains vague, despite the fact that it is clearly an important parameter in evaluating models in general and game-theoretic results in particular. Here we want to make it a bit less vague by offering a graphic measure for a particular kind of robustness— ‘matrix robustness’— using a three dimensional display of the universe of 2 x 2 game theory. In a display of this form, familiar games such as the Prisoner’s Dilemma, Stag Hunt, Chicken and Deadlock (...) appear as volumes, making comparison easy regarding the extent of different game-theoretic effects. We illustrate such a comparison in robustness between the triumph of Tit for Tat in a spatialized environment (Grim 1995, Grim, Mar, and St. Denis 1998) and a spatialized modeling of the Contact Hypothesis regarding prejudice reduction (Grim, et. al 2005a, 2005b). The geometrical representation of relative robustness also offers a possibility for links between geometrical theorems and results regarding robustness in game theory. (shrink)

We apply spatialized game theory and multi-agent computational modeling as philosophical tools: (1) for assessing the primary social psychological hypothesis regarding prejudice reduction, and (2) for pursuing a deeper understanding of the basic mechanisms of prejudice reduction.

It is shown that the power set of $\kappa$ ordered by the subset relation modulo various versions of the non-stationary ideal can be embedded into the partial order of Borel equivalence relations on $2^\kappa$ under Borel reducibility. Here $\kappa$ is an uncountable regular cardinal with $\kappa^{<\kappa}=\kappa$.

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game . Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game , by a simple and natural interpretation . Jervell proposed another type of a combinatorial game, by (...) abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω = ϵ0) in the Veblen hierarchy of ordinals. (shrink)

The main aim of the text is to show how a game of Go (Weiqi, baduk, Igo) can serve as a model representation of the ontological-metaphysical aspect of the actor–network theory (ANT). An additional objective is to demonstrate in return that this ontological-metaphys⁠ical aspect of ANT represented on Go/Weiqi game model is able to highlight the key aspect of this theory—onto-methodological praxis.

In previous work I’ve defended an interest-relative theory of belief. This paper continues the defence. It has four aims. -/- 1. To offer a new kind of reason for being unsatis ed with the simple Lockean reduction of belief to credence. 2. To defend the legitimacy of appealing to credences in a theory of belief. 3. To illustrate the importance of theoretical, as well as practical, interests in an interest-relative account of belief. 4. To revise my account to cover (...) propositions that are practically and theoretically irrelevant to the agent. (shrink)

If semantic consequence is analyzed with extensive games, logical reasoning can be accounted for by looking at how players solve entailment games. However, earlier approaches to game semantics cannot achieve this reduction, by want of explicitly dened preferences for players. Moreover, although entailment games can naturally translate the idea of argumentation about a common ground, a cognitive interpretation is undermined by the complexity of strategic reasoning. We thus describe a class of semantic extensive entailment game with (...) algorithmic players, who have preferences for parsimonious spending of computational resources and thus compute partial strategies under qualitative uncertainty about future histories. We prove the existence of local preferences for moves and of strategic fixpoints that allow to map game-trees to tableaux proofs, and exhibit a strategy prole that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We then discuss the correspondence between proof heuristics and strategies in our games, the relations of our games to gts, and possible extensions to other entailment relations. We conclude that the main interest of our result lies in the possibility to bridge argumentative and cognitive models of logical reasoning, rather than in new meta-theoretic results. All proofs are given in appendix. (shrink)

Oikkonen, J. and J. Väänänen, Game-theoretic inductive definability, Annals of Pure and Applied Logic 65 265-306. We use game-theoretic ideas to define a generalization of the notion of inductive definability. This approach allows induction along non-well-founded trees. Our definition depends on an underlying partial ordering of the objects. In this ordering every countable ascending sequence is assumed to have a unique supremum which enables us to go over limits. We establish basic properties of this induction and examine examples where it (...) emerges naturally. In the main results we prove an abstract Kleene Theorem and restricted versions of the Stage-Comparison Theorem and the Reduction Theorem. (shrink)

Norm Phelps has long been one of the leading theoreticians, historians, and strategists of the animal advocacy movement. His new book collects his recent writings on this subject, as well as offers in print for the first time a fully revised and updated version of the e-book he published with Lantern in 2013 (978-1-59056-379-3). Phelps argues that faced with the overwhelming wealth and power of the animal exploitation industries, animal activists are like David trying to stand up to Goliath. But (...) rather than following the unsuccessful strategies of the past, Phelps proposes that we change the game by adopting David's strategy of refusing to play by Goliath's rules. Additional essays explore class and race in animal advocacy, the place of public policy vs. private morality in creating social change, and the unyielding barrier of human exceptionalism. Trenchant, wise, and deeply committed to the reduction of suffering and the liberation of animals, Changing the Game is sure to offer animal advocates much food for thought as the movement charts a way forward for all sentient beings. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Suitors' GamesRuth ScodelScholars disagree about the goals of Penelope's suitors in the Odyssey-do they seek kingship, Odysseus' property, Penelope herself, or some combination? This disagreement is unsurprising: different passages imply different goals. Twice the suitors speak of dividing Odysseus' property (2.335-36, 16.384-86). In other passages, however, the kingship seems to be at issue; so Telemachus says that Eurymachus "is most eager to marry my mother and possess the (...) honor [geras] of Odysseus" (15.521-22)-which would seem to imply that he would have all Odysseus' wealth as well. Other passages stress the suitors' sexual desire for Penelope (1.365-66, 18.212-13). Hence scholars have often emphasized one aspect of the suitors' aims. Some think that Penelope herself is a mere excuse and the suitors' real desire is kingship in Ithaca.1 Others argue that Penelope is the only object and that "kingship" does not even exist.2 Many believe that Penelope and the kingship are somehow connected, and that the suitors seek both, while some admit that they are perplexed.3 The poet's failure to clarify Penelope's motives complicates the issue even further and has led to even more debate. Is she as loyal to [End Page 307] Odysseus as the poet claims? If so, why has she led the suitors on? Why does she appear before them in book 18? Why does she choose to hold the bow contest when there are so many indications of Odysseus' imminent return?4Scholars, however, have made the problems worse by assuming a single underlying situation. The suitors' actions, and those of Penelope, are easier to understand if we follow the narrative with the expectation that the characters adapt to changing situations. There are three basic situations in the poem, and so three "games." The first we must reconstruct, because Telemachus' new assertiveness ends it as the poem starts. His declaration of hostility toward the suitors and his attempt to use the assembly against them mark the transition to a new game. This game, too, fails to achieve an outcome, when the suitors fail to kill Telemachus on his return and an omen warns them against trying again. The third game begins when Penelope's appearance before the suitors inflames their desire for her and leads to the bow contest.I borrow the term "game" from the game theory widely used in the social sciences.5 In game theory, a "game" is a rule-governed situation in which each person must make choices in the knowledge that other people are also choosing and that the outcome depends in a prescribed way on all the choices. Game theory assumes "instrumental rationality": without considering why people want what they want, it assumes that people have preferences and use rational means to achieve them.6 Ends do not need to be rational, but means do. A rigorous application of game theory to a literary text would be foolishly reductive. Furthermore, game theory would require assigning a quantitative value to each possible outcome for each player. Still, a perspective influenced by game theory can clarify what strategies are available to the characters and the rationality or lack of rationality of their choices. [End Page 308]This argument treats the characters as possible people for whom the audience infers rational motives, provided that the narrator does not provide other motivations and such inferences offer an adequate explanation for otherwise confusing actions. This is the easiest way to discuss the narrative sequence, and it is not an inappropriate procedure for the authorial audience of this poem.7 After all, the Odyssey celebrates the cleverest of heroes and implies that Odysseus' wife resembles him. Without imagining people who calculate quite as tidily as the analysis does, we may still see them as consciously evaluating their options. However, even interpreters who reject the view of the characters as rational choosers may find this analysis helpful. They may, for example, see the characters as behaving more intuitively than through calculation yet still find it useful to examine how far their actions conform to a rational model. Even if the characters' motives are bracketed, this discussion seeks to... (shrink)

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of game terms to a certain (...) ‘minimal canonical form’, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities. (shrink)

There are many social psychological theories regarding the nature of prejudice, but only one major theory of prejudice reduction: under the right circumstances, prejudice between groups will be reduced with increased contact. On the one hand, the contact hypothesis has a range of empirical support and has been a major force in social change. On the other hand, there are practical and ethical obstacles to any large-scale controlled test of the hypothesis in which relevant variables can be manipulated. Here (...) we construct a spatialized model that tests the core hypothesis in a large array of game-theoretic agents. Robust results offer a new kind of support for the contact hypothesis: results in simulation do accord with a hypothesis of reduced prejudice with increased contact. The spatialized game-theoretic model also suggests a deeper explanation for at least some of the social psychological phenomena at issue. (shrink)

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2 × 2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those (...) class='Hi'>games. The measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation . New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling . Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19 , 95–125). (shrink)

We tackle the problem of preservation of totality by composition in arena games. We first explain how this problem reduces to a finiteness theorem on what we call pointer structures, similar to the parity pointer functions of Harmer, Hyland and Mélliès and the interaction sequences of Coquand. We discuss how this theorem relates to normalization of linear head reduction in simply-typed lambda-calculus, leading us to a semantic realizability proof à la Kleene of our theorem. We then present another (...) proof of a more combinatorial nature. Finally, we discuss the exact class of strategies to which our theorems apply. (shrink)

Let o(κ) denote the Mitchell order of κ. We show how to reduce long games which run to the first ordinal admissible in the play, to iteration games on models with a cardinal κ so that (1) κ is a limit of Woodin cardinals: and (2) o(κ) = κ⁺⁺. We use the reduction to derive several optimal determinacy results on games which run to the first admissible in the play.

Are games essentially a form of make-believe, or essentially an act of struggling against obstacles? There have been several attempts to reduce one of these accounts to the other. Kendall Walton has argued for the primacy of the make-believe account of games. Even when we are struggling against obstacles in games, says Walton, we are engaged in a form of make-believe: we are making believe that these lines are real obstacles, that these points really matter. Bernard Suits (...) has argued for the primacy of the account of games as struggling against obstacles. Even when we are making believe in games, says Suits, we are still engaged in act act of struggling against obstacles. Usually we are struggling to keep the narrative going. I argue that Walton's and Suits' reductive attempts are both wrong: that there are two distinct activities, of making-believe and struggling against obstacles, neither of which is wholly reducible to a subset of the other. Importantly, in many games we are engaged in both making-believe and struggling against obstacles. But there are some games that are pure struggle with no make-believe (like games of real survival in the real wilderness). And there are games of pure make-believe, in which there are no obstacles or struggle. (shrink)

I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show how the equilibrium concepts differ, computing necessary (...) and sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. (shrink)

Harm-reduction approaches are used to reduce the burden of risky human behaviour without necessarily aiming to stop the behaviour. We discuss what an introduction of harm reduction for doping in sports would mean in parallel with a relaxation of the antidoping rule. We analyse what is ethically at stake in the following five levels: (1) What would it mean for the athlete (the self)? (2) How would it impact other athletes (the other)? (3) How would it affect the (...) phenomenon of sport as a game and its fair play basis (the play)? (4) What would be the consequences for the spectator and the role of sports in society (the display)? and (5) What would it mean for what some consider as essential to being human (humanity)? For each level, we present arguments for and against doping and then discuss what a harm-reduction approach, within a dynamic regime of a partially relaxed antidoping rule, could imply. We find that a harm-reduction approach is morally defensible and potentially provides a viable escape out of the impasse resulting from the impossibility of attaining the eradication of doping. The following question remains to be answered: Would a more relaxed position, when combined with harm-reduction measures, indeed have less negative consequences for society than today9s all-out antidoping efforts that aim for abstinence? We provide an outline of an alternative policy, allowing a cautious step-wise change to answer this question and then discuss the ethical aspects of such a policy change. (shrink)

Any theory of reduction that goes only so far as carried in Parts I and II does only half the job. Prima facie at least, there are cases of would-be reduction which seem torn between two conflicting intuitions. On the one side there is a strong intuition that reduction is involved, and a strongly retentive reduction at that. On the other side it seems that the concepts at one level cross-classify those at the other level, so (...) that there is no way to identify properties at one level with those at the other. There is evidence to suggest that there will be no unique mental state/neural state association that can be set up, because, e.g., many different parts of the nervous system are all capable of taking over ‘control’ of the one mental function. And it is alleged that infinitely many, worse: indefinitely many, different bio-chemo-physical states could correspond to the economic property ‘has a monetary system of economic exchange’; and similarly for the property ‘has just won a game of tennis’. Yet one doesn't want an economic system or a game of tennis to be some ghostly addition to the actual bio-chemo-physical processes and events involved. Similarly one hopes that neurophysiology allied with the rest of natural science will render human experience and behaviour explicable. (shrink)

Character customization is a prominent feature in digital games, affording users the ability to tailor one’s virtual self-representation (avatar) to match aspects of their actual or ideal self, influencing psychological well-being. The mental health implications of character customization can be partially explained by self-discrepancy theory, which argues that achieving congruence with one’s avatar reduces cognitive dissonance. However, the role of undesirable self-concepts such as mental health ailments have largely been overlooked in this context despite forming part of one’s identity. (...) In theory, customization of an avatar representing undesirable self-concepts presents a self-regulatory paradox: individuals desire to reduce discrepancies with a self-representation, yet they also desire to enlarge discrepancies with a disliked-self. To reconcile this, two experiments explored the psychological implications of imbuing avatars with undesirable self-concepts. In Study 1 (N= 90), participants customized an avatar to represent anxiety within themselves (i.e., an anxiety avatar). Customization significantly reduced state anxiety compared to a control group, supporting the proposed discrepancy-reduction mechanism. Study 2 (N= 122) employed a 2 (customization: yes, no) × 2 (destruction: yes, no) between-subjects design, with participants either destroying or observing an anxiety avatar. Destruction of customized anxiety avatars resulted in the largest reduction in anxiety among all conditions, supporting the proposed discrepancy-enlargement mechanism. Theoretical and practical implications for the use of avatar-based e-mental health interventions are discussed. (shrink)

I present a semantics for the language of first-order additive-multiplicative linear logic, i.e. the language of classical first-order logic with two sorts of disjunction and conjunction. The semantics allows us to capture intuitions often associated with linear logic or constructivism such as sentences = games, SENTENCES = resources or sentences = problems, where “truth” means existence of an effective winning strategy.The paper introduces a decidable first-order logic ET in the above language and gives a proof of its soundness and (...) completeness with respect to this semantics. Allowing noneffective strategies in the latter is shown to lead to classical logic.The semantics presented here is very similar to Blass's game semantics. Although there is no straightforward reduction between the two corresponding notions of validity, my completeness proof can likely be adapted to the logic induced by Blass's semantics to show its decidability, which was the main problem left open in Blass's paper.The reader needs to be familiar with classical logic and arithmetic. (shrink)

Climate negotiations under the United Nations Framework Convention on Climate Change have so far failed to achieve a robust international agreement to reduce greenhouse gas emissions. Game theory has been used to investigate possible climate negotiation solutions and strategies for accomplishing them. Negotiations have been primarily modelled as public goods games such as the Prisoner’s Dilemma, though coordination games or games of conflict have also been used. Many of these models have solutions, in the form of equilibria, (...) corresponding to possible positive outcomes—that is, agreements with the requisite emissions reduction commitments. Other work on large-scale social dilemmas suggests that it should be possible to resolve the climate problem. It therefore seems that equilibrium selection may be a barrier to successful negotiations. Here we use an N-player bargaining game in an agent-based model with learning dynamics to examine the past failures of and future prospects for a robust international climate agreement. The model suggests reasons why the desirable solutions identified in previous game-theoretic models have not yet been accomplished in practice and what mechanisms might be used to achieve these solutions. (shrink)

Why do we seek out and enjoy uncertain success in playing games? Game designers and researchers suggest that games whose challenges match player skills afford engaging experiences of achievement, competence, or effectance—ofdoing well. Yet, current models struggle to explain why such balanced challenges best afford these experiences and do not straightforwardly account for the appeal of high- and low-challenge game genres like Idle and Soulslike games. In this article, we show that Predictive Processing (PP) provides a coherent (...) formal cognitive framework which can explain the fun in tackling game challenges with uncertain success as the dynamic process of reducing uncertainty surprisingly efficiently. In gameplay as elsewhere, people enjoydoing better than expected, which can track learning progress. In different forms, balanced, Idle, and Soulslike games alike afford regular accelerations of uncertainty reduction. We argue that this model also aligns with a popular practitioner model, Raph Koster’sTheory of Fun for Game Design, and can unify currently differentially modelled gameplay motives around competence and curiosity. (shrink)

ContextThe recent development of “serious games” has produced encouraging results in maintaining adherence to health-related interventions. In alcohol research, several studies have shown that computerized training on attentional bias decreases alcohol consumption bias among students. However, these highly controlled experimental situations, do not allow for direct large-scale dissemination. Our objective is to evaluate an attentional bias remediation program using a gamified smartphone training procedure.MethodsFifty students from Clermont-Ferrand University were invited to participate in the study. After a cognitive assessment in (...) the laboratory, the smartphone application was installed on each Student’s smartphone. Participants were randomly assigned to either the alcohol attentional training group or the control group Each student had to complete the 2-min program at least once a day for 15 days. After 15 days, a new cognitive assessment of attention bias was conducted in the laboratory. Forty-seven students were included in the study.ResultsOur analyses did not show any effect of the cognitive remediation program on attentional bias reduction between the two group [F < 1, p = 0.87], attentional performance [F = 1.63, p = 0.20] or inhibitory abilities [F < 1, p = 0.73]. These results were confirmed by Bayesian analyses.DiscussionDespite the absence of group effects, both the alcohol and control version of this program appeared to reduce attentional bias and increase inhibition capacities in the subset of participants who had attentional bias for alcohol at baseline This pilot study identifies areas for improvement in smartphone applications for future developments. Attentional bias remediation programs remain an interesting way to explore. (shrink)

In human groups performing oscillatory tasks, it has been observed that the frequency of participants' oscillations reduces when compared to that acquired in solo. This experimental observation is not captured by the standard Kuramoto oscillators, often employed to model human synchronization. In this work, we aim at capturing this observed phenomenon by proposing three alternative modifications of the standard Kuramoto model that are based on three different biologically-relevant hypotheses underlying group synchronization. The three models are tuned, validated and compared against (...) experiments on a group synchronization task, which is a multi-agent extension of the so-called mirror game. (shrink)

Kaneko-Suzuki developed epistemic logics of shallow depths with multiple players for investigations of game theoretical problems. By shallow depth, we mean that nested occurrences of belief operators of players in formulae are restricted, typically to be of finite depths, by a given epistemic structure. In this paper, we develop various methods of surgical operations (cut and paste) of epistemic world models. An example is a bouquet-making, i.e., tying several models into a bouquet. Another example is to engraft a model to (...) some branches of another model. By these methods, we obtain various meta-theorems on semantics and syntax on epistemic logics. To illustrate possible uses of our meta-theorems, we present one game theoretical theorem, which is also a meta-theorem in the sense of logic. (shrink)

In the context of propositional logics, we apply semantics modulo satisfiability—a restricted semantics which comprehends only valuations that satisfy some specific set of formulas—with the aim to efficiently solve some computational tasks. Three possible such applications are developed.We begin by studying the possibility of implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through semantics modulo satisfiability. We theoretically investigate some approaches to such representation concept, called representation modulo satisfiability, and describe a polynomial algorithm that builds representations in the newly (...) introduced system. An implementation of the algorithm, test results and ways to randomly generate rational McNaughton functions for testing are presented. Moreover, we propose an application of such representations to the formal verification of properties of neural networks by means of the reasoning framework of Łukasiewicz Infinitely-valued Logic.Then, we move to the investigation of the satisfiability of joint probabilistic assignments to formulas of Łukasiewicz Infinitely-valued Logic, which is known to be an NP-complete problem. We provide an exact decision algorithm derived from the combination of linear algebraic methods with semantics modulo satisfiability. Also, we provide an implementation for such algorithm for which the phenomenon of phase transition is empirically detected.Lastly, we study the game theory situation of observable games, which are games that are known to reach a Nash equilibrium, however, an external observer does not know what is the exact profile of actions that occur in a specific instance; thus, such observer assigns subjective probabilities to players actions. We study the decision problem of determining if a set of these probabilistic constraints is coherent by reducing it to the problems of satisfiability of probabilistic assignments to logical formulas both in Classical Propositional Logic and Łukasiewicz Infinitely-valued Logic depending on whether only pure equilibria or also mixed equilibria are allowed. Such reductions rely upon the properties of semantics modulo satisfiability. We provide complexity and algorithmic discussion for the coherence problem and, also, for the problem of computing maximal and minimal probabilistic constraints on actions that preserves coherence.prepared by Sandro Márcio da Silva Preto.E-mail: [email protected]:https://doi.org/10.11606/T.45.2021.tde-17062021-163257. (shrink)

We show, for any ordinal γ ≥ 3, that the class RaCAγ is pseudo-elementary and has a recursively enumerable elementary theory. ScK denotes the class of strong subalgebras of members of the class K. We devise games, Fⁿ (3 ≤ n ≤ ω), G, H, and show, for an atomic relation algebra A with countably many atoms, that Ǝ has a winning strategy in Fω(At(A)) ⇔ A ∈ ScRaCAω, Ǝ has a winning strategy in Fⁿ(At(A)) ⇐ A ∈ ScRaCAn, (...) Ǝ has a winning strategy in G(At(A)) ⇐ A ∈ RaCAω, Ǝ has a winning strategy in H(At(A)) ⇒ A ∈ RaRCAω for 3 ≤ n < ω. We use these games to show, for γ ≥ 5 and any class K of relation algebras satisfying RaRCAγ ⊆ K ⊆ ScRaCA₅, that K is not closed under subalgebras and is not elementary. For infinite γ, the inclusion RaCAγ ⊂ ScRaCAγ is strict. For infinite γ and for a countable relation algebra A we show that A has a complete representation if and only if A is atomic and Ǝ has a winning strategy in F(At(A)) if and only if A is atomic and A ∈ ScRaCAγ. (shrink)

Failed expectations about “bringing in the Kingdom” may lie at the root of the decline in the missionary force of mainline denominations. Is a missiological motivation based on “evangelising the world to bring back the King” giving rise to similar unrealistic expectations? Optimistic statistics on aspects of church growth are vulnerable to question. Reports of the numbers of missionaries forget the aspect of proportionality to size of population, reports of church growth include the effect of babies born to Christians of (...) all denominational groups, and increases in the numbers of missionaries include short-termers. The growth of the new category of Great Commission Christians and the reduction in number of unreached people groups are based on faulty descriptive bases. If the world remains unevangelised by 2001, these attempts to motivate Christians to evangelism on the basis of current optimistic statistical improvements will undermine a proper basis for motivating people for evangelism which is based on faith and not on sight. (shrink)

Axelord’s [(1970), Conflict of Interest, Markham Publishers, Chicago] index of conflict in 2 × 2 games with two pure strategy equilibria has the property that a reduction in the cost of holding out corresponds to an increase in conflict. This article takes the opposite view, arguing that if losing becomes less costly, a player is less likely to gamble to win, which means that conflict will be less frequent. This approach leads to a new power index and a (...) new measure of stubbornness, both anchored in strategic reasoning. The win probability defined as power constitutes an equilibrium refinement which differs from Harsanyi and Selten’s [(1988), A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge] refinement. In contrast, Axelrod’s approach focuses on preferences regarding divergences from imaginary outmost rewards that cannot be obtained jointly. The player who is less powerful in an asymmetric one-shot game becomes more powerful in the repeated game, provided he or she values the future sufficiently more than the opponent. This contrasts with the view that repetition induces cooperation, but conforms with the expectation that a more patient player receives a larger share of the pie. (shrink)

This study aimed to explore the mediating effects of internet gaming disorder, social network use, and generalized pathological internet use on the association between loneliness and depression. A total of 2211 junior high school students completed questionnaires regarding loneliness, internet gaming disorder, social network use, GPIU, and depression. The results of a structural equation model revealed that the path coefficient of loneliness to depression was significantly positive, loneliness could not predict depression through GPIU directly, but loneliness could predict depression through (...) internet gaming disorder to GPIU, loneliness could predict depression through social network use to GPIU, and loneliness could not predict depression through internet gaming disorder to social network use to GPIU. These results provided significant implications for the prevention and reduction of depression in Chinese junior high school students. (shrink)

Let κ be a singular cardinal. Karp's notion of a chain model of size κ is defined to be an ordinary model of size κ along with a decomposition of it into an increasing union of length cf. With a notion of satisfaction and -isomorphism such models give an infinitary logic largely mimicking first order logic. In this paper we associate to this logic a notion of a dynamic EF-game which gauges when two chain models are chain-isomorphic. To this game (...) is associated a tree which is a tree of size κ with no κ-branches -branches). The measure of how non-isomorphic the models are is reflected by a certain order on these trees, called reduction. We study the collection of trees of size κ with no κ-branches under this notion and prove that when cf = ω this collection is rather regular; in particular it has universality number exactly κ+. Such trees are then used to develop a descriptive set theory of the space cf κ. The main result of the paper gives in the case of κ strong limit singular an exact connection between the descriptive set-theoretic complexity of the chain isomorphism orbit of a model, the reduction order on the trees and winning strategies in the corresponding dynamic EF games. In particular we obtain a neat analog of the notion of Scott watershed from the Scott analysis of countable models. (shrink)

The purpose of this study was to empirically investigate the interrelationships between push and pull factors associated with the consumption of women’s professional basketball games. Multiple factors pertaining to sport consumers’ internal needs, identified as “push” factors, contain various intangible socio-psychological motivations representing an individual’s intrinsic desires that drive consumers toward certain goal-driven behaviors. On the other hand, “pull” factors, related to the supply side, refer to the different aspects of sport products the management of sport teams provides. It (...) is imperative to obtain a better understanding of the push–pull interaction so that sport marketers can design their products to satisfy spectators’ expectations with different needs. Spectators attending WNBA games responded to an on-site survey. CFA was conducted to ensure the psychometric properties of the scales, which showed that the overall model fit the data well. A canonical correlation analysis was performed, and two significant functions were revealed by the dimension reduction analysis. The first function [F = 4.49, p < 0.001]: I-Want-Everything-Consumer suggests that the market segment comprises individuals with multiple needs and expectations, both of which need to be met simultaneously. Thus, sports marketers can satisfy WNBA consumers’ needs by enhancing the quality of tangible pull factors. The second function [F = 2.38, p < 0.001]: Achievement-Seekers revealed that the consumers motivated by vicarious achievement expect game promotion rather than the quality of the opposing team, indicating that sport marketers should provide tailored promotional strategies to satisfy this segment of consumers. Specifically, the findings of this study can be used to segment consumers based upon fan motives and position products accordingly by managing the controllable aspects of sport products. This study provides empirical evidence of the relationship between WNBA consumers’ multiple needs and attributes associated with the WNBA core product. (shrink)

Despite the challenges associated with virtually mediated communication, remote collaboration is a defining characteristic of online multiplayer gaming communities. Inspired by the teamwork exhibited by players in first-person shooter games, this study investigated the verbal and behavioral coordination of four-player teams playing a cooperative online video game. The game, Desert Herding, involved teams consisting of three ground players and one drone operator tasked to locate, corral, and contain evasive robot agents scattered across a large desert environment. Ground players could (...) move throughout the environment, while the drone operator’s role was akin to that of a “spectator” with a bird’s-eye view, with access to veridical information of the locations of teammates and the to-be-corralled agents. Categorical recurrence quantification analysis was used to measure the communication dynamics of teams as they completed the task. Demands on coordination were manipulated by varying the ground players’ ability to observe the environment with the use of game “fog.” Results show that catRQA was sensitive to changes to task visibility, with reductions in task visibility reorganizing how participants conversed during the game to maintain team situation awareness. The results are discussed in the context of future work that can address how team coordination can be augmented with the inclusion of artificial agents, as synthetic teammates. (shrink)

If, as many suppose, pornography changes people, a question arises as to how.1 One answer to this question offers a grand and noble vision. Inspired by the idea that pornography is speech, and inspired by a certain liberal ideal about the point of speech in political life, some theorists say that pornography contributes to that liberal ideal: pornography, even at its most violent and misogynistic, and even at its most harmful, is political speech that aims to express certain views about (...) the good life, 2aims to persuade its consumers of a certain political point of view—and to some extent succeeds in persuading them. Ronald Dworkin suggests that the pornographer contributes to the ‘moral environment, by expressing his political or social convictions or tastes or prejudices informally’, that pornography ‘seeks to deliver’ a ‘message’ , that it reflects the ‘opinion’ that ‘women are submissive, or enjoy being dominated, or should be treated as if they did’, that it is comparable to speech ‘advocating that women occupy inferior roles’.3 Pornography on this view is political speech that aims to persuade its listeners of the truth of certain ideas about women, and of course ‘the government must leave to the people the evaluation of ideas’.4 Another answer offers a vision that is not grand and noble, but thoroughly reductive. Pornography is not politically persuasive speech, but speech that works by a process of psychological conditioning. This view seems common enough in the social science literature. Consider, for example, this description of an early experiment, from a time that pre-dates contemporary political debate. (shrink)

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.

For countable structures U and B, let $\mathfrak{U}\overset{\alpha}{\rightarrow}\mathfrak{B}$ abbreviate the statement that every Σ0 α (Lω1,ω) sentence true in U also holds in B. One can define a back and forth game between the structures U and B that determines whether $\mathfrak{U}\overset{\alpha}{\rightarrow}\mathfrak{B}$ . We verify that if θ is an Lω,ω sentence that is not equivalent to any Lω,ω Σ0 n sentence, then there are countably infinite models U and B such that $\mathfrak{U} \vDash \theta, \mathfrak{B} \vDash \neg \theta$ , (...) and $\mathfrak{U}\overset{n}{\rightarrow}\mathfrak{B}$ . For countable languages L there is a natural way to view L structures with universe ω as a topological space, XL. Let [U] = {B ∈ XL∣B ≅ U} denote the isomorphism class of U. Let U and B be countably infinite nonisomorphic L structures, and let $C \subseteq \omega^\omega$ be any Π0 α subset. Our main result states that if $\mathfrak{U}\overset{\alpha}{\rightarrow}\mathfrak{B}$ , then there is a continuous function f: ωω → XL with the property that $x \in C \Rightarrow f(x) \in \lbrack\mathfrak{U}\rbrack$ and $x \notin C \Rightarrow f(x) \in \lbrack\mathfrak{B}\rbrack$ . In fact, for α ≤ 3, the continuous function f can be defined from the $\overset{\alpha}{\rightarrow}$ relation. (shrink)

We present a self‐contained analysis of some reduction games, which characterise various natural subclasses of the first Baire class of functions ranging from and into 0‐dimensional Polish spaces. We prove that these games are determined, without using Martin's Borel determinacy, and give precise descriptions of the winning strategies for Player I. As an application of this analysis, we get a new proof of the Baire's lemma on pointwise convergence.

This chapter takes inspiration from Wittgenstein’s thinking to formulate a non-reductive toolbox for the study of religion associated with generative modelling, specifically as applied in complex adaptive systems theory. It converges on a communal perspective on religion as multiscale active inference that contrasts starkly with common ‘straw person’ perspectives on religion that reduce it to ‘erroneous’ theorising generated by the brain. In contrast, we argue, religious practices at the enculturated level of description involve implicit and explicit meanings, experienced both individually (...) and collectively. Firstly, we characterise these in terms of Wittgenstein’s notions of rule-following and language games. Secondly, we discuss how the collective and perspectival aspects of religion in enculturation with morals, doctrines, rituals, and expressions can be formalised in terms of deep active inference in multi-agent systems. This approach describes how religions are incommensurable with scientific methods due to the epistemic separation between the different kinds of language games of religious and scientific practices. Their touchpoints tend to give rise to perpetual confusion and unproductive discussions, requiring perspicuous presentations that can be formulated with our toolbox. In this sense, our account has implications for tackling complex societal challenges such as ethical policy-making. (shrink)

Analytic processes reduce biases, but it is not known how or when these processes will be deployed. Based on an affective signal hypothesis, relatively strong affective reactions were expected to result in increased analytic processing and reduced bias in judgement. The valence and strength of affective reactions were manipulated through varying outcomes in a game or evaluative conditioning of a stimulus. Relatively strong positive or negative affective reactions resulted in less desirability bias. Bias reduction only occurred if participants had (...) time to deploy analytic processes and indicators of the degree of analytic processing (in the form of attentional control) predicted less bias. Affective processes have long been acknowledged as a source of bias, but these findings suggest affective processes are also integral to bias reduction. (shrink)

Two prevalent assumptions in the philosophy of sport literature are that all sports are games and that all games are contests, meant to determine who is the better at the skills definitive of the sport. If these are correct, it would follow that all sports are contests and that a range of sporting activities, including nature sports, are not in fact sports at all. This paper first confronts the notion that sport and games must seek to resolve (...) skill superiority through consideration of sport activities that have no such aim. The reduction of sport to game is also shown to be untenable and due to misunderstanding the point of sport activities, specifically, why people engage in them. This leads to reconsideration of the dominance of an instrumental conception of sport and the pursuit of excellence as anthropomaximising efficiency. The Norwegian tradition of frilutsliv is explored as a counterpoint to both conventional and nature sport. (shrink)

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well-known Kirby-Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well-quasi-ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap-embeddability in terms of provability logic due to Lev (...) Beklemishev is also presented. (shrink)

We investigate the definability in monadic ∑11 and monadic Π11 of the problems REGk, of whether there is a regular subgraph of degree k in some given graph, and XREGk, of whether, for a given rooted graph, there is a regular subgraph of degree k in which the root has degree k, and their restrictions to graphs in which every vertex has degree at most k, namely REGkk and XREGkk, respectively, for k ≥ 2 . Our motivation partly stems from (...) the fact that REGkk and XREGkk are logspace equivalent to CONN and REACH, respectively, for k ≥ 3, where CONN is the problem of whether a given graph is connected and REACH is the problem of whether a given graph has a path joining two given vertices. We use monadic first - order reductions, monadic ∑11 games and a recent technique due to Fagin, Stockmeyer and Vardi to almost completely classify whether these problems are definable in monadic ∑11 and monadic Π11, and we compare the definability of these problems. (shrink)

Could a person ever transcend what it is like to be in the world as a human being? Could we ever know what it is like to be other creatures? Questions about the overcoming of a human perspective are not uncommon in the history of philosophy. In the last century, those very interrogatives were notably raised by American philosopher Thomas Nagel in the context of philosophy of mind. In his 1974 essay What is it Like to Be a Bat?, Nagel (...) offered reflections on human subjectivity and its constraints. Nagel’s insights were elaborated before the social diffusion of computers and could not anticipate the cultural impact of technological artefacts capable of materializing interactive simulated worlds as well as disclosing virtual alternatives to the “self.” In this sense, this article proposes an understanding of computers as epistemological and ontological instruments. The embracing of a phenomenological standpoint entails that philosophical issues are engaged and understood from a fundamentally practical perspective. In terms of philosophical praxis, or “applied philosophy,” I explored the relationship between human phenomenologies and digital mediation through the design and the development of experimental video games. For instance, I have conceptualized the first-person action-adventure video game Haerfest (Technically Finished 2009) as a digital re-formulation of the questions posed in Nagel’s famous essay. Experiencing a bat’s perceptual equipment in Haerfest practically corroborates Nagel’s conclusions: there is no way for humans to map, reproduce, or even experience the consciousness of an actual bat. Although unverifiable in its correspondence to that of bats, Haerfest still grants access to experiences and perceptions that, albeit still inescapably within the boundaries of human kinds of phenomenologies, were inaccessible to humans prior to the advent of computers. Phenomenological alterations and virtual experiences disclosed by interactive digital media cannot take place without a shift in human kinds of ontologies, a shift which this study recognizes as the fundamental ground for the development of a new humanism (I deem it necessary to specify that I am not utilizing the term “humanism” in its common connotation, that is to say the one that emerged from the encounter between the Roman civilization and the late Hellenistic culture. According to this conventional acceptation, humanism indicates the realization of the human essence through “scholarship and training in good conduct” (Heidegger 1998, p. 244). However, Heidegger observed that this understanding of humanism does not truly cater to the original essence of human beings, but rather “is determined with regard to an already established interpretation of nature, history, world, and […] beings as a whole.” (Heidegger 1998, p. 245) The German thinker found this way of embracing humanism reductive: a by-product of Western metaphysics. As Heidegger himself specified in his 1949 essay Letter on Humanism, his opposition to the traditional acceptation of the term humanism does not advocate for the “inhuman” or a return to the “barbaric” but stems instead from the belief that the humanism can only be properly understood and restored in culture as more original way of meditating and caring for humanity and understanding its relationship with Being.). Additionally, this study explicitly proposes and exemplifies the use of interactive digital technology as a medium for testing, developing and disseminating philosophical notions, problems and hypotheses in ways which are alternative to the traditional textual one. Presented as virtual experiences, philosophical concepts can be accessed without the filter of subjective imagination. In a persistent, interactive, simulated environment, I claim that the crafting and the mediation of thought takes a novel, projective (In Martin Heidegger’s 1927 Being and Time, the term “projectivity” indicates the way a Being opens to the world in terms of its possibilities of being (Heidegger 1962, pp. 184–185, BT 145). Inspired by Heidegger’s and Vilem Flusser’s work in the field of philosophy of technology as well as Helmuth Plessner’s anthropological position presented in his 1928 book Die Stufen des Organischen und der Mensch. Einleitung in die philosophische Anthropologie, this study understands the concept of projectivity as the innate openness of human beings to construct themselves and their world by means of technical artefacts. In this sense, this study proposes a fundamental understanding of technology as the materialization of mankind’s tendency to overcome its physical, perceptual and communicative limitations.) dimension which I propose to call “augmented ontology.”. (shrink)