We consider ω n -automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of length ω n for some integer n ≥ 1. We show that all these structures are ω-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation for ω 2 -automatic (resp. ω n -automatic for n > 2) boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non (...) commutative groups) is not determined by the axiomatic system ZFC. We infer from the proof of the above result that the isomorphism problem for ω n -automatic boolean algebras, n ≥ 2, (respectively, rings, commutative rings, non commutative rings, non commutative groups) is neither a ${\mathrm{\Sigma }}_{2}^{1}-\mathrm{s}\mathrm{e}\mathrm{t}$ nor a ${\mathrm{\Pi }}_{2}^{1}-\mathrm{s}\mathrm{e}\mathrm{t}$ . We obtain that there exist infinitely many ω n -automatic, hence also ω-tree-automatic, atomless boolean algebras $\mathcal{B}_{n}$ , n ≥ 1, which are pairwise isomorphic under the continuum hypothesis CH and pairwise non isomorphic under an alternate axiom AT, strengthening a result of [14]. (shrink)

While classical temporal logics lose track of a state as soon as a temporal operator is applied, several branching-time logics able to repeatedly refer to a state have been introduced in the literature. We study such logics by introducing a new formalism, hybrid branching-time logics, subsuming the other approaches and making the ability to refer to a state more explicit by assigning a name to it. We analyze the expressive power of hybrid branching-time logics and the complexity of their satisfiability (...) problem. As main result, the satisfiability problem for the hybrid versions of several branching-time logics is proved to be 2EXPTIME -complete. To prove the upper bound, the automata-theoretic approach to branching-time logics is extended to hybrid logics. As a result of independent interest, the nonemptiness problem for alternating one-pebble Büchi tree automata is shown to be 2EXPTIME -complete. A common property of the logics studied is that they refer to only one state. This restriction is crucial: The ability to refer to more than one state causes a nonelementary blow-up in complexity. In particular, we prove that satisfiability for NCTL * has nonelementary complexity. (shrink)

We consider games over a finite alphabet with Gurevich-Harrington's winning conditions and restraints as in Yakhnis-Yakhnis . The game tree, the Gurevich-Harrington's kernels of the winning condition and the restraints are defined by finite automata. We give an effective criterion to determine the winning player and an effective presentation of a class of finite automata defined winning strategies.Our approach yields an alternative solution to the games considered by Büchi and Landweber . The BL algorithm is an important (...) tool for solving effectively presented games. The differences between the BL and our algorithms are as follows. Our algorithm is uniformly applicable to winning sets that correspond to boolean combinations of BL winning conditions, while the BL algorithm requires a transformation of such boolean combinations into a single BL condition. Our algorithm directly applies to a larger class of game trees for a given game alphabet than does the BL one. We describe Büchi-Landweber's class of winning conditions in a more transparent way by using finite automata and Gurevich-Harrington's form of winning conditions. Our algorithms that determine the winner of the game and find a winning strategy, are based on a translation of the events in the game in terms of the transition table of the automaton representing the game. This automaton differs from the ones that represent BL winning conditions. Both algorithms need further investigation.The algorithm determining the winner in the game, can be used as a verifier of concurrent programs. This is because programs can be viewed as strategies in Gurevich-Harrington's games and program specifications could be regarded as winning conditions for such games. The algorithm which finds a winning strategy could be used as a basis for automated concurrent program design.The present paper is a sequel to Annals of Pure and Applied Logic 48 277–297. (shrink)

In program synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, then at each moment it reads input signals and writes output signals, which depend on the input signals and the history of the computation so far. The specification considers all possible input sequences. Thus, if the specification is linear, it should hold in every computation generated by the interaction, and if the specification is branching, it should hold in (...) the tree that embodies all possible input sequences. Often, the system cannot read all the input signals generated by its environment. For example, in a distributed setting, it might be that each process can read input signals of only part of the underlying processes. Then, we should transform a specification into a system whose output depends only on the readable parts of the input signals and the history of the computation. This is called synthesis with incomplete information. In this work we solve the problem of synthesis with incomplete information in its full generality. We consider linear and branching settings with complete and incomplete information. We claim that alternation is a suitable and helpful mechanism for coping with incomplete information. Using alternating tree automata, we show that incomplete information does not make the synthesis problem more complex, in both the linear and the branching paradigm. In particular, we prove that independently of the presence of incomplete information, the synthesis problems for CTL and CTL * are complete for EXPTIME and 2EXPTIME, respectively. (shrink)

We present a variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall. The cooperation modalities assume the use the distributed knowledge of coalitions and accordingly refer to perfect recall incomplete information strategies. We propose a model-checking algorithm for the logic. It is based on techniques for games with imperfect information and partially observable objectives, and involves deciding emptiness for automata on infinite trees. We also propose an axiomatic system and (...) prove its completeness for a rather expressive subset. As for the constructs left outside this completely axiomatised subset, we present axioms by which they can be defined in the subset on the class of models in which every state has finitely many successors and give a complete axiomatisation for a “flat” subset of the logic with these constructs included. (shrink)

In the automata-theoretic approach to verification, we translate specifications to automata. Complexity considerations motivate the distinction between different types of automata. Already in the 60s, it was known that deterministic Büchi word automata are less expressive than nondeterministic Büchi word automata. The proof is easy and can be stated in a few lines. In the late 60s, Rabin proved that Büchi tree automata are less expressive than Rabin tree automata. This proof (...) is much harder. In this work we relate the expressiveness gap between deterministic and nondeterministic Büchi word automata and the expressiveness gap between Büchi and Rabin tree automata. We consider tree automata that recognize derived languages. For a word language L, the derived language of L, denoted L, is the set of all trees all of whose paths are in L. Since often we want to specify that all the computations of the program satisfy some property, the interest in derived languages is clear. Our main result shows that L is recognizable by a nondeterministic Büchi word automaton but not by a deterministic Büchi word automaton iff L is recognizable by a Rabin tree automaton and not by a Büchi tree automaton. Our result provides a simple explanation for the expressiveness gap between Büchi and Rabin tree automata. Since the gap between deterministic and nondeterministic Büchi word automata is well understood, our result also provides a characterization of derived languages that can be recognized by Büchi tree automata. Finally, it also provides an exponential determinization of Büchi tree automata that recognize derived languages. (shrink)

Using the concept of progress measure, we give a new proof of Rabin's fundamental result that the languages defined by tree automata are closed under complementation. To do this we show that for certain infinite games based on tree automata, an immediate determinacy property holds for the player who is trying to win according to a Rabin acceptance condition. Immediate determinancy is stronger than the forgetful determinacy of Gurevich and Harrington, which depends on more information about (...) the past, but applies to another class of games. Next, we show a graph theoretic duality theorem for winning conditions. Finally, we present an extended version of Safra's determinization construction. Together, these ingredients and the determinacy of Borel games yield a straightforward recipe for complementing tree automata. Our construction is almost optimal, i.e. the state space blow-up is essentially exponential- thus roughly the same as for automata on finite or infinite words. To our knowledge, no prior constructions have been better than double exponential. (shrink)

We provide a translation from SNFPLTL, a normal form for propositional linear time temporal logic, into alternating automata on infinite words, and vice versa. We show this translation has the property that the set of SNFPLTL clauses is satisfiable if and only if the alternating automaton has an accepting run. As there is no direct method known for checking the non-emptiness of alternating automata, the translation to SNFPLTL, together with a temporal proof on the resulting (...) SNFPLTL clauses, provides an indirect non-emptiness check for alternating automata. (shrink)

We study satisfiability and infinite-state model checking in ICPDL, which extends Propositional Dynamic Logic (PDL) with intersection and converse operators on programs. The two main results of this paper are that (i) satisfiability is in 2EXPTIME, thus 2EXPTIME-complete by an existing lower bound, and (ii) infinite-state model checking of basic process algebras and pushdown systems is also 2EXPTIME-complete. Both upper bounds are obtained by polynomial time computable reductions to ω-regular tree satisfiability in ICPDL, a reasoning problem that we introduce (...) specifically for this purpose. This problem is then reduced to the emptiness problem for alternating two-way automata on infinite trees. Our approach to (i) also provides a shorter and more elegant proof of Danecki's difficult result that satisfiability in IPDL is in 2EXPTIME. We prove the lower bound(s) for infinite-state model checking using an encoding of alternating Turing machines. (shrink)

Bilingualism has been identified as a potential cognitive factor linked to delayed onset of dementia as well as boosting executive functions in healthy individuals. However, more recently, this claim has been called into question following several failed replications. It remains unclear whether these contradictory findings reflect how bilingualism is defined between studies, or methodological limitations when measuring the bilingual effect. One key issue is that despite the claims that bilingualism yields general protection to cognitive processes, studies reporting putative bilingual differences (...) are often focused on domain specific experimental paradigms. This study chose a broader approach, by considering the consequences of bilingualism on a wide range of cognitive functions within individuals. We utilised 19 measures of different cognitive functions commonly associated with bilingual effects, to form a “cognitive profile” for 215 non-clinical participants. We recruited Welsh speakers, who as a group of bilinguals were highly homogeneous, as means of isolating the bilingualism criterion. We sought to determine if such analyses would independently classify bilingual/monolingual participant groups based on emergent patterns driven by collected cognitive profiles, such that population differences would emerge. Multiple predictive models were trained to independently recognise the cognitive profiles of bilinguals, older adults and higher education attainment. Despite managing to successfully classify cognitive profiles based on age and education, the model failed to differentiate between bilingual and monolingual cognitive ability at a rate greater than that of chance. Repeated modelling using alternative definitions of bilingualism, and just the older adults, yielded similar results. In all cases then, using our “bottom–up” analytical approach, there was no evidence that bilingualism as a variable indicated differential cognitive performance – as a consequence, we conclude that bilinguals are not cognitively different from their monolingual counterparts, even in older demographics. We suggest that studies that have reported a bilingual advantage could well have confounded other key variables that may be driving reported advantages. We recommend that future research refine the machine learning methods used in this study to further investigate the complex relationship between bilingualism and cognition. (shrink)

We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.

Flooding is one of the most damaging natural hazards globally. During the past three years, floods have claimed hundreds of lives and millions of dollars of damage in Iran. In this study, we detected flood locations and mapped areas susceptible to floods using time series satellite data analysis as well as a new model of bagging ensemble-based alternating decision trees, namely, bag-ADTree. We used Sentinel-1 data for flood detection and time series analysis. We employed twelve conditioning parameters of elevation, (...) normalized difference’s vegetation index, slope, topographic wetness index, aspect, curvature, stream power index, lithology, drainage density, proximities to river, soil type, and rainfall for mapping areas susceptible to floods. ADTree and bag-ADTree models were used for flood susceptibility mapping. We used software of Sentinel application platform, Waikato Environment for Knowledge Analysis, ArcGIS, and Statistical Package for the Social Sciences for preprocessing, processing, and postprocessing of the data. We extracted 199 locations as flooded areas, which were tested using a global positioning system to ensure that flooded areas were detected correctly. Root mean square error, accuracy, and the area under the ROC curve were used to validate the models. Findings showed that root mean square error was 0.31 and 0.3 for ADTree and bag-ADTree techniques, respectively. More findings illustrated that accuracy was obtained as 86.61 for bag-ADTree model, while it was 85.44 for ADTree method. Based on AUC, success and prediction rates were 0.736 and 0.786 for bag-ADTree algorithm, in order, while these proportions were 0.714 and 0.784 for ADTree. This study can be a good source of information for crisis management in the study area. (shrink)

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception . These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — is (...) not adequate, and a new approach is necessary. A study of finite deterministic automata without initial states is exactly the aim of this paper. We will define and investigate the complexity of various types of simulations between automata. Minimal automata will be constructed and proven to be unique up to an isomorphism. We will build our results on an extension of Myhill-Nerode technique; all constructions will make use of “automata responses” to simple experiments only, i.e., no information about the internal machinery will be considered available. (shrink)

We present an alternative proof that from large cardinals, we can force the tree property at $\kappa ^+$ and $\kappa ^{++}$ simultaneously for a singular strong limit cardinal $\kappa $. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for $\kappa =\aleph _{\omega ^2}$.

Since Aristotle, it has been common to understand wonder as a psychological state characterized by an absence of rational understanding. Drawing on this idea, a number of historians have suggested that the wonder which had long characterized the experience of automata, declined in the early modern period alongside the increased availability of theoretical treatises on mechanics. This article seeks to challenge this view by examining the relationship between rational and practical modes of technical understanding in John Wilkins’ Mathematicall Magick (...) (1648). My aim is to show that a close reading of the second book of the Mathematicall Magick reveals an alternative conception of wonder as an experience of skilled workmanship that both tolerates theoretical understanding and is increased through practical experience. It will be my claim that the conception of technical wonder which emerges from Wilkin’s descriptions of automata, reveals how the concept of Aristotelian wonder is too reductive to capture the variety of ways in which mechanical technology was experienced in early modern England. (shrink)

This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.

This project explores the extent to which trees can be seen as a solution to global environmental crisis. The physical component of this project involved growing over 300 fruit trees from seed and planting them throughout Mora county, Costa Rica. This report represents the theoretical component of the project, in which the author reflects on the lessons that can be drawn from the act of planting a tree, in order to add complexity to what is often used as cultural (...) shorthand for an uncontroversial environmental virtue. Originally conceived as an opportunity to offset the author’s carbon emissions from a lifetime of airline travel, an examination of the literature reveals the practical ambiguity of this short-term goal. The author concludes that while trees do provide many physical benefits for their surrounding microclimate, including their ability to promote the flow of water, air and carbon, they cannot address our planetary crisis without larger cultural change. The metaphors that trees convey may therefore be just as vital as the physical services they provide. Among these are the necessity of addressing the root causes of environmental crisis, how small microclimatic changes create resilient plant communities, and the way planting a seed offers an alternative to the insatiable search for an action that is “good enough” to save the planet. (shrink)

Ernst Mayr’s influence on philosophy of biology has given the field a particular perspective on evolution, phylogeny and life in general. Using debates about the tree of life as a guide, I show how Mayrian evolutionary biology excludes numerous forms of life and many important evolutionary processes. Hybridization and lateral gene transfer are two of these processes, and they occur frequently, with important outcomes in all domains of life. Eukaryotes appear to have a more tree-like history because successful (...) lateral events tend to occur among more closely related species, or at a lower frequency, than in prokaryotes, but this is a difference of degree rather than kind. Although the tree of life is especially problematic as a representation of the evolutionary history of prokaryotes, it can function more generally as an illustration of the limitations of a standard evolutionary perspective. Moreover, for philosophers, questions about the tree of life can be applied to the Mayrian inheritance in philosophy of biology. These questions make clear that the dichotomy of life Mayr suggested is based on too narrow a perspective. An alternative to this dichotomy is a multidimensional continuum in which different strategies of genetic exchange bestow greater adaptiveness and evolvability on prokaryotes and eukaryotes. (shrink)

Has Christianity, a religion with incarnation at its heart, devalued the flesh through an over-emphasis on the cross? In this article Lisa Isherwood's response is an overwhelming 'yes'. Isherwood argues that the devaluation of the flesh has hindered Christianity's efforts to address the genocidal realities of global capitalism. She suggests that a return to the tree found in Eden and sensuously engaged with by our foremother Eve, will provide a sounder base for the development of a Christo-ethic that can (...) offer alternatives to advanced capitalism. (shrink)

Political violence does not end with the last death. A common feature of mass murder has been the attempt at destroying any memory of victims, with the aim of eliminating them from history. Perpetrators seek not only to eliminate a perceived threat, but also to eradicate any possibility of alternate, competing social and national histories. In his timely and important book, Unchopping a Tree, Ernesto Verdeja develops a critical justification for why transitional justice works. He asks, “What is the (...) balance between punishment and forgiveness? And, “What are the stakes in reconciling?” Employing a normative theory of reconciliation that differs from prevailing approaches, Verdeja outlines a concept that emphasizes the importance of shared notions of moral respect and tolerance among adversaries in transitional societies. Drawing heavily from cases such as reconciliation efforts in Latin America and Africa—and interviews with people involved in such efforts—Verdeja debates how best to envision reconciliation while remaining realistic about the very significant practical obstacles such efforts face Unchopping a Tree addresses the core concept of respect across four different social levels—political, institutional, civil society, and interpersonal—to explain the promise and challenges to securing reconciliation and broader social regeneration. (shrink)

The thesis focuses on a quite recent research field lying in between Descriptive Set Theory and Automata Theory (for infinite objects). In both areas, one is often concerned with subsets of the Cantor space or of its homeomorphic copies. In Descriptive Set Theory, such subsets are usually stratified in topological hierarchies, like the Borel hierarchy, the Wadge hierarchy and the difference hierarchy; in Automata Theory, such sets are studied in terms of regularity, that is, the property of being (...) recognised by an automaton or, equivalently, of being expressible in Monadic Second-Order Logic. This double point of view leads to many interesting questions about the interplay and relationship between topological complexity and regularity. While we have a complete picture of what happens in the case of automata on words, the case of automata on trees is still a terra incognita. Some results have already been obtained for particular classes of languages, like Buchi languages, deterministic languages, ¨ and unambiguous languages. In this thesis we instead drop any restriction and prove some new results concerning arbitrary regular tree languages which belong to low levels of the Borel hierarchy and of the Wadge hierarchy. (shrink)

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, (...) such as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. ​. (shrink)

Care is more than dispensing pills or cleaning beds. It is about responding to the entire patient. What is called “bedside manner” in medical personnel is a quality of treating the patient not as a mechanism but as a being—much like the caregiver—with desires, ideas, dreams, aspirations, and the gamut of mental and emotional character. As automata, answering an increasing functional need in care, are designed to enact care, the pressure is on their becoming more humanlike to carry out (...) the function more effectively. The question becomes not merely whether the care automaton can effect good bedside manner but whether the patient’s response is not feeling deceived by the humanlikeness. It seems the device must be designed either to effect explicit mere human-“likeness,” thus likely undermining its bedside-manner potential, or to fool the patient completely. Neither option is attractive. This article examines the social problems of designing maximally humanlike care automata and how problems may start to erode the human rights of users/patients. The article then investigates the alternatives for dealing with this problem, whether by industrial and professional self-regulation or public-policy initiatives. It then frames the problem in the broader historical perspective in terms of previous bans, moratoria, and other means of control of hazardous and potentially rights-violating techniques and materials. (shrink)

In this article the author claims that Waluchow’s “living tree constitutionalism” constitutes a “copernican revolution in our thinking”, because it provides not a mere common law theory of judicial review but a general theory of judicial review and of constitutional democracy. Although agrees that something like the common law methodology is at play here, disagrees on characterizing it as bottom-up. Accordingly, intends to praise the main aspiration of A Common Law Theory of Judicial Review: The Living Tree, i.e. (...) to provide a better understanding of charters and judicial re- view in a constitutional democracy by “the living tree” metaphor; to appraise an unwarranted claim, i.e. to reduce it to the common law bottom-up methodology; and, to raise the alternative with a friendly amendment, i.e. to identify the community’s constitutional political morality via, a method that is both bottom-up and top-down, which is already explicit —or at least implicit— in his account.Resumen:En este artículo el autor sostiene que el “constitucionalismo del árbol viviente” de Waluchow constituye una “revolución copernicana en nuestro pensamiento”, dado que proporciona no sólo una teoría del judicial review, sino una teoría general del judicial review y de la democracia. No obstante que el autor coincide en que en esta teoría de Waluchow existe un lugar para una metodología del common law, discrepa en caracterizarla como una que va de “abajo hacia arriba”. Por lo tanto, el objetivo del artículo es resaltar la importancia del argumento principal del libro A Common Law Theory of Judicial Review: The Living Tree por medio del cual se intenta proporcionar un mejor entendimiento de las garantías individuales y del judicial review, pero advertir una consecuencia innecesaria, es decir, reducir la explicación a una metodología del common law de “abajo hacia arriba”. A su vez el autor pretende proporcionar una corrección amigable: identificar la moralidad política constitucional de la comunidad a través de un método que es tanto de “abajo hacia arriba” como de “arriba hacia abajo”, metodología que se encuentra implícita en el libro de Waluchow. (shrink)

Tree diagrams are the prevailing form of visualization in biological classification and phylogenetics. Already during the time of the so-called Systematist Wars from the mid-1960s until the 1980s most journal articles and textbooks published by systematists contained tree diagrams. Although this episode of systematics is well studied by historians and philosophers of biology, most analyses prioritize scientific theories over practices and tend to emphasize conflicting theoretical assumptions. In this article, I offer an alternative perspective by viewing the conflict (...) through the lens of representational practices with a case study on tree diagrams that were used by numerical taxonomists (phenograms) and cladists (cladograms). I argue that the current state of molecular phylogenetics should not be interpreted as the result of a competition of views within systematics. Instead, molecular phylogenetics arose independently of systematics and elements of cladistics and phenetics were integrated into the framework of molecular phylogenetics, facilitated by the compatibility of phenetic and cladistic practices with the quantitative approach of molecular phylogenetics. My study suggests that this episode of scientific change is more complex than common narratives of battles and winners or conflicts and compromises. Today, cladograms are still used and interpreted as specific types of molecular phylogenetic trees. While phenograms and cladograms represented different forms of knowledge during the time of the Systematist Wars, today they are both used to represent evolutionary relationships. This indicates that diagrams are versatile elements of scientific practice that can change their meaning, depending on the context of use within theoretical frameworks. (shrink)

In this article the author aims to assess Wilfrid J. Waluchow’s more recent book, by depicting its main aim, namely to provide a better understanding of judicial review in a constitutional democracy via the “living tree” metaphor; by disapproving an unwarranted claim, purposely to reduce the metaphor to the common law (bottom-up) methodology; and by re-developing his alternative, specifically to identify the community’s constitutional political morality, with a friendly amendment, which is already explicit —or at least somehow implicit— on (...) it, i.e. not only by judges but also by legislators, including framers, amenders or reformers, and other legal officials, including lawyers and citizens, which at the end will grant him the point.Resumen:En este artículo el autor intenta evaluar el libro más reciente de Wilfrid J. Waluchow, al caracterizar su objetivo principal, a saber: proporcionar una mejor explicación del control judicial de la constitucionalidad en una democracia constitucional mediante la metáfora del “árbol viviente”; al cuestionar un argumento, precisamente el que reduce dicha metáfora a la metodología (de abajo hacia arriba) del common law; y, al re-desarrollar una alternativa, específicamente al identificar la moralidad política constitucional de la comunidad, a partir de una enmienda amigable, misma que ya está explícita —o hasta cierto punto implícita— en ella, i. e. no sólo por los juzgadores sino también por los legisladores, incluidos los constituyentes originarios y revisores o reformadores, y otros operadores jurídicos, incluidos abogados y ciudadanos, lo cual al final de cuentas le dará el punto. (shrink)

Journal of Mathematical Logic, Volume 24, Issue 03, December 2024. We study which [math]-distributive forcing notions of size [math] can be embedded into tree Prikry forcing notions with [math]-complete ultrafilters under various large cardinal assumptions. An alternative formulation — can the filter of dense open subsets of a [math]-distributive forcing notion of size [math] be extended to a [math]-complete ultrafilter.

Jennifer Johnston’s fiction presents the conditions of Irish culture and society by exploring the separations between interior and exterior realms and past and present temporalities persisting within the insulating privacy of the familial home space. In _The Christmas Tree_ (1981), the home is both haven and prison for Johnston’s heroine. In this paper, I argue that the home—which assumes the form of the individual body and the familial home—is paradoxical. The protagonist leaves 1950s Ireland because of the country’s rigid gender (...) roles in order to pursue an autonomous life as a writer in England, but she is unable to publish her writing within the confines of the patriarchal publishing world. The home of her body becomes paradoxical when she becomes a single mother as an avenue for creativity but is then diagnosed with terminal cancer. She returns to her father’s home to die, which she re-orders and reclaims through the disorder of the uncanny—represented by her non-conformity and illness brought into the patriarchal home. By writing her life story and creating a brief, alternative maternal relationship with her young caretaker, the protagonist confronts her own ambivalence toward her parents, who also represent aspects of oppressive heteronormative gender expectations. (shrink)

Considering the properties of mirror neurons (MNs) in terms of development and phylogeny, we offer a novel, unifying, and testable account of their evolution according to the available data and try to unify apparently discordant research, including the plasticity of MNs during development, their adaptive value and their phylogenetic relationships and continuity. We hypothesize that the MN system reflects a set of interrelated traits, each with an independent natural history due to unique selective pressures, and propose that there are at (...) least three evolutionarily significant trends that gave raise to three subtypes: hand visuomotor, mouth visuomotor, and audio–vocal. Specifically, we put forward a mosaic evolution hypothesis, which posits that different types of MNs may have evolved at different rates within and among species. This evolutionary hypothesis represents an alternative to both adaptationist and associative models. Finally, the review offers a strong heuristic potential in predicting the circumstances under which specific variations and properties of MNs are expected. Such predictive value is critical to test new hypotheses about MN activity and its plastic changes, depending on the species, the neuroanatomical substrates, and the ecological niche. (shrink)

We introduce a cyclic proof system for the two-way alternation-free modal μ-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule. The global effect of backwards modalities on traces is handled by making the semantics relative to a specific strategy of the opponent in the evaluation game. This allows us to augment sequents by so-called trace atoms, describing traces that the proponent can construct against the opponent’s strategy. The (...) idea for trace atoms comes from Vardi’s reduction of alternating two-way automata to deterministic one-way automata. Using the multi-focus annotations introduced earlier by Marti and Venema, we turn this trace-based system into a path-based system. We prove that our system is sound for all sequents and complete for sequents not containing trace atoms. (shrink)

When people understand a counterfactual such as “if the flowers had been roses, the trees would have been orange trees,” they think about the conjecture, “there were roses and orange trees,” and they also think about its opposite, the presupposed facts. We test whether people think about the opposite by representing alternates, for example, “poppies and apple trees,” or whether models can contain symbols, for example, “no roses and no orange trees.” We report the discovery of an inference‐to‐alternates effect—a tendency (...) to make an affirmative inference that refers to an alternate even from a negative minor premise, for example, “there were no orange trees, therefore there were poppies.” Nine experiments show the inference‐to‐alternates effect occurs in a binary context, but not a multiple context, and for direct and indirect reference; it can be induced and reduced by prior experience with similar inferences, and it also occurs for indicative conditionals. The results have implications for theories of counterfactual conditionals, and of negation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 20 (2000) 151-165 [Access article in PDF] Santayana and Buddhism: The Choice between the Cross and the Bo Tree Paul Grimley KuntzEmory UniversitySantayana honors Gotama Buddha as a profound religious genius as well as an original philosopher. Gotama's way is genuine spiritual wisdom, and constantly compared with Christian mysticism as a way of enlightenment. It is therefore understandable that a Spaniard, who learned his catechism in (...) Ávila, and who was educated in the New England of Emerson and other Transcendentalists who honored Oriental wisdom, should have so much to say about the Buddha and Buddhism.The effort of this paper is to gather many of the isolated passages to give a coherent picture of Santayana and Buddhism. One difficulty to be overcome is that the philosopher rarely quotes his sources (the exception is a single quotation from Dasgupta). Although Santayana has numerous opinions, he does not reveal on which translations he has relied. Nor does he contrast different traditions of Buddhists. To overcome the vagueness of scholarship, I have used the volumes found in Widener Library: the sorts of books known to Santayana's dissertation director, Josiah Royce, and those of a sympathetic sort that had led Santayana as early as the writing of his dissertation on Rudolf Hermann Lotze to reject the latter's defiantly Christian and Western contempt for oriental "superstition." The sympathy can be expressed as similar to that of Schopenhauer in reading the Upanishads or Wilhelm von Humboldt in studying the Bhagavadgita. Santayana's study makes him aware of his Catholicism but he is unlike the Jesuit Dahlmann who attacks Buddhism as Nihilism. Santayana is more like his contemporaries who worked in psychology and philosophy of religion. Although Friedrich Heiler's work 1 and writings of James Bissett Pratt 2 were a bit too late to have influenced Santayana, comparison serves to illuminate and strengthen Santayana's conclusions. Perhaps Heiler is even more appropriate because Buddhistic insights remind him of those of St. Theresa. Santayana would support Pratt's view that Nirvana is not the annihilation of all desire but the extinguishing of evil passions. What Santayana finds congenial in Christian Neo-Platonism and in Spinoza, as well as in Buddhism, is the achievement of freedom of the spirit. 3 It has become a commonplace of world history that the two greatest founders of religion whose ways of salvation triumphed in Europe and in Asia respectively are the Christ and the Buddha. Philosophers of religion like Heiler accept both as saviors with a universal message, one, Jesus "the master of prayer" ("der Meister des Gebets"), the [End Page 151] other, Gotama "the master of contemplation" ("der Meister der Versenking"). Santayana is not concerned with the fact of the success of their missions, for there are indeed other triumphs such as Mohammed's Islam, and if it be classified as a religion, Marx's Communism. Santayana is hardly offering his services as a philosophic mediator, as Whitehead tries to do in Religion in the Making, to bring the two communities of faith to a closer approximation of a truly universal religion. 4Santayana reveals great personal depth as he ponders the contrast between the Gospel and the Fourfold Noble Truth. What is the appeal of Christ on the Cross dying "to save us?" What is the appeal of "the serene Buddha, lifting the finger of meditation and profound counsel?" 5 These questions are asked in a meditation in Soliloquies in England in the sympathetic way of those American philosophers who like Pratt have the option of remaining Christian or converting to Buddhism. William James might well have patted Santayana on the back for struggling with the alternatives, for wrestling with a live option. Probably because of Buddha's message of truth, Santayana has shifted from religion as poetry, which James considered "rotten," to how "a general truth about existence and experience" is symbolized poetically, which James would consider healthy.In answering the question "What does the cross signify?" Santayana strips away the "various analogies, legal, sentimental, or chivalrous," and he... (shrink)

We study which [Formula: see text]-distributive forcing notions of size [Formula: see text] can be embedded into tree Prikry forcing notions with [Formula: see text]-complete ultrafilters under various large cardinal assumptions. An alternative formulation — can the filter of dense open subsets of a [Formula: see text]-distributive forcing notion of size [Formula: see text] be extended to a [Formula: see text]-complete ultrafilter.

This study investigates the extent to which there is individuality in how structural variation is conditioned over time. Earlier research already classified the diachronically unstable gerund variation as involving a high fraction of mixed-usage speakers throughout the change, whereby the proportion of the conservative variant versus the progressive variant as observable in the linguistic output of individual language users superficially resembles the mean proportion as observable at the population level. However, this study sets out to show that there can still (...) be heterogeneity within such a centralized population in terms of how each individual conditions the observed variation. A random forest and conditional inference tree analysis of over 14,000 gerunds uttered by nineteen seventeenth-century authors is presented to show that, while the most important language-internal factors conditioning the gerund variation are adopted by (and shared between) all authors, we can still attest inter-individual variation (i) at lower levels of variable importance, and (ii) in the breadth of the range of contexts individual authors employ to condition the attested variation. (shrink)

The improvement of the welfare of inhabitants of arid and semi-arid lands, either through the enhancement of existing livelihoods or the promotion of alternative ones, and their potential constraints are discussed. Alternative livelihoods are discussed under regenerative and extractive themes with respect to environmental stability. Regenerative (i.e., non-extractive) livelihoods include activities like apiculture, poultry keeping, pisciculture, silkworm production, drought tolerant cash cropping, horticulture, community wildlife tourism, processing of livestock and crop products, agro-forestry for tree products, and micro-enterprises in the (...) informal sector. Examples of livelihoods that are extractive or potentially so include timber production, woodcarving, basketry, brick making, sand scooping, and charcoal making. Suggestions to improve these livelihoods in a sustainable manner are offered. (shrink)

This paper sets out to launch a challenge to the usual ‘modernist’ view of the relationship between ecology and ethics. Two ‘post-modern’ interpretations of this relationship are considered. The first ‘deep’ interpretation holds that ecology reveals that nature has intrinsic value. The second interpretation derives from the work of Michel Foucault. The aim of his critique is to reveal how certain values are taken for granted by the acceptance of certain scientific models, and how the acceptance of those models as (...) true makes it impossible to articulate alternative values. I end by suggesting, contra Foucault, that phenomenological enquiry could serve to articulate alternative and perhaps more eco-friendly values. (shrink)

Contemporary generative grammar assumes that syntactic structure is best described in terms of sets, and that locality conditions, as well as cross-linguistic variation, is determined at the level of designated functional heads. Syntactic operations (merge, MERGE, etc.) build a structure by deriving sets from lexical atoms and recursively (and monotonically) yielding sets of sets. Additional restrictions over the format of structural descriptions limit the number of elements involved in each operation to two at each derivational step, a head and a (...) non-head. In this paper, we will explore an alternative direction for minimalist inquiry based on previous work, e.g., Frank (2002, 2006), albeit under novel assumptions. We propose a view of syntactic structure as a specification of relations in graphs, which correspond to the extended projection of lexical heads; these are _elementary trees_ in Tree Adjoining Grammars. We present empirical motivation for a lexicalised approach to structure building, where the units of the grammar are elementary trees. Our proposal will be based on cross-linguistic evidence; we will consider the structure of elementary trees in Spanish, English and German. We will also explore the consequences of assuming that nodes in elementary trees are addresses for purposes of tree composition operations, substitution and adjunction. (shrink)

So, C. I don’t know that T. Premises 1 and 2 are both plausible. However, C seems false—I do seem to know that there is a tree before me. AI presents a puzzle because its two plausible premises yield a conclusion whose negation is plausible. And no matter whether we accept or reject AI, we find that we must give up something plausible—either premise 1, premise 2, or the negation of C. But which of these should we give up? (...) I call this question the skeptical puzzle.1 Recently, Mark Heller2 has argued that we can solve the skeptical puzzle by giving up premise 2. I argue, however, that Heller does not adequately respond to an objection to his proposed solution. I go on to argue that we can solve the skeptical puzzle by giving up premise 1. (shrink)

Why do otherwise well-intentioned managers make decisions that have negative social or environmental consequences? To answer this question, the authors combine the literature on construal level theory with the compromise effect to explore the circumstances that lead to seemingly unethical decision-making. The results of two studies suggest that the degree to which managers make high-risk tradeoffs is highly influenced by how they mentally represent the decision context. The authors find that managers are more likely to make seemingly unethical tradeoffs when (...) psychological distance is high (rather than low) and when they are forced to choose between competing alternatives. However, when given the option not to choose, managers better reflect on the consequences of each alternative, and thus become more likely to choose options with less risk of negative consequences. The results suggest that simply offering managers the option not to choose may reduce psychological distance and help organizations avoid seemingly unethical decision-making. (shrink)

Language sciences have long maintained a close and supposedly necessary coupling between the infinite productivity of the human language faculty and recursive grammars. Because of the formal equivalence between recursion and non-recursive iteration; recursion, in the technical sense, is never a necessary component of a generative grammar. Contrary to some assertions this equivalence extends to both center-embedded relative clauses and hierarchical parse trees. Inspection of language usage suggests that recursive rule components in fact contribute very little, and likely nothing significant, (...) to linguistic creativity. Further than this, if the productivity of human language is considered as not rigidly bound, but not infinite, then the need for any sort of iteration in generative grammars vanishes and can be replaced with a Non-iterative Explicit Alternatives Rule grammar. The knock-on effects of dispensing with recursive grammar components are: that language diversity can simply be based on rule and lexicon combinatorics with no potentially infinite dimensions derived from recursive or iterative components of rules; the oddity of a vast, multiply-infinite competence set of ‘grammatical but unacceptable’ productions is gone; and the development of a language faculty based on rules that eschew iterative rule components avoids any need for explaining ‘special’ mechanisms. On the broader front of searching for the mechanisms of mind, our analysis can be similarly applied to the proposals for a recursive basis for mind as an explanation for humanity’s great leap forward. (shrink)

This dissertation will compare the concept of nature as it appears in the philosophies of the American pragmatist John Dewey and the Chinese daoist Zhuangzi and will defend two central claims. The first of these is that Dewey and Zhuangzi share a view of nature that is non-reductive, philosophically liberal, and more comprehensive than the accounts recurrent in much of the Western tradition. This alternate conception of nature is non-reductive in the way that it avoids the physically mechanistic outlook underwriting (...) much of contemporary Anglo-American thought. It is philosophically liberal in that it accepts a more generous and progressive position than predominant Western orthodoxies. And, it is more comprehensive in scope insofar as it draws as much from the social sciences as it does from the natural sciences. The second claim defended will be that the synoptic vision gained from such a comparison offers a new heuristic program for research into the philosophical position known as naturalism, a program that can, at once, avoid the scientistic tendencies of the current, mainstream treatment of nature and reconnect with earlier, more inclusive models. Where Dewey's and Zhuangzi's ideas converge, one finds similarities in the prescriptions each made for human action, and where they differ, one finds mutually complementary insights. Finally, this heuristic will be used to refute various interpretations of Dewey and Zhuangzi that tend to understate or ignore the importance of nature within their schemes. (shrink)

Propositional dynamic logic (PDL) is one of the most successful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, as long-known, reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context (...) of description logics, and prove that satisfiability is decidable and EXPTIME-complete using an approach based on Büchi tree automata. (shrink)

While monadic second-order logic (MSO) has played a prominent role in model theoretic syntax, modal logics have been used in this context since its inception. When comparing propositional dynamic logic (PDL) to MSO over trees, Kracht (1997) noted that there are tree languages that can be defined in MSO that can only be defined in PDL by adding new features whose distribution is predictable. He named such features “inessential features”. We show that Kracht’s observation can be extended to other (...) modal logics of trees in two ways. First, we demonstrate that for each stronger logic, there exists a tree language that can only be defined in a weaker logic with inessential features. Second, we show that any tree language that can be defined in a stronger logic, but not in some weaker logic, can be defined with inessential features. Additionally, we consider Kracht’s definition of inessential features more closely. It turns out that there are features whose distribution can be predicted, but who fail to be inessential in Kracht’s sense. We will look at ways to modify his definition. (shrink)

Various theories of moral cognition posit that moral intuitions can be understood as the output of a computational process performed over structured mental representations of human action. We propose that action plan diagrams—“act trees”—can be a useful tool for theorists to succinctly and clearly present their hypotheses about the information contained in these representations. We then develop a methodology for using a series of linguistic probes to test the theories embodied in the act trees. In Study 1, we validate the (...) method by testing a specific hypothesis (diagrammed by act trees) about how subjects are representing two classic moral dilemmas and finding that the data support the hypothesis. In Studies 2–4, we explore possible explanations for discrete and surprising findings that our hypothesis did not predict. In Study 5, we apply the method to a less well‐studied case and show how new experiments generated by our method can be used to settle debates about how actions are mentally represented. In Study 6, we argue that our method captures the mental representation of human action better than an alternative approach. A brief conclusion suggests that act trees can be profitably used in various fields interested in complex representations of human action, including law, philosophy, psychology, linguistics, neuroscience, computer science, robotics, and artificial intelligence. (shrink)

For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated restricted variables called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.We construct an axiomatic system for this (...) extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc. (shrink)