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Schützenberger's theorem for the ordinary RSK correspondence naturally extends to Chen et. al's correspondence for matchings and partitions. Thus the counting of bilaterally symmetric $k$-noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for $3$-noncrossing partitions, we use a different technique to develop a $\mathsf{MAPLE}$ package for $2$-dimensional vacillating lattice walk enumeration problems. As an application, we find an interesting relation between two special bilaterally symmetric partitions.

We use mosaics to provide a simple, sound, complete and terminating tableau reasoning procedure for the temporal logic of until and since over general linear time. [ABSTRACT FROM AUTHOR]

Abstract: Software engineering research is driven by the aim of making software development more dynamic, flexible and evolvable. Nowadays the emphasis is on the evolution of pre-existing sub-systems and component and service-based development, where often only a part of the system is totally under control of the designer, most components being remotely operated by external vendors. In this context, we tackle the following problem: given the formal specification of the (incomplete) system, say it , already built, how to characterize collaborators of to be selected, based on a given communication interface , so that a given property is satisfied. Using properties described by temporal logic formulae and systems by CCS processes, if is the formula to be satisfied by the complete system, an efficient and automatic procedure is defined to identify a formula such that, for each existing process satisfying , the process satisfies . Important features of this result are simplicity of the derived property , compared to the original one, and scalability of the verification process. Such characteristics are necessary for applying the method to both incremental design and system evolution scenarios where is already in place, and one needs to understand the specification of the functionality of the new component that should correctly interact with . Indeed, in general, finding a suitable partner for is easier than finding a complete system satisfying the global property. Moreover, in this paper it is shown how can be used also to select a set of possible candidate processes through a property-directed and structural heuristic. From the verification point of view, the description of the lacking component through a logic formula guarantees correctness of the integration with of any process that exhibits a behaviour compliant with the inferred formula. [Copyright &y& Elsevier]

We develop a conceptually clear, intuitive and feasible decision procedure for testing satisfiability in the full multiagent epistemic logic CMAEL(CD) with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for CMAEL(CD) and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input set of formulae of CMAEL(CD) and closes for every unsatisfiable input set of formulae. [ABSTRACT FROM AUTHOR]

This article analyses the state of dependency between the tableau and the image. The proposed ideas go against the normal understanding, usage and function of the image and follow instead a particular ontological understanding of the image. This ontological analysis of the image is irritated by the presupposition that the ontological difference and distinctness of the image is not fixed and secure; on the contrary, it is conditioned by change, as is the case with all beings, being or beingness. This ontological difference exists and is only in its ontic manifestations. Furthermore, the article underlines the fact that the image, as a mode of being, is a plastic being that can be blocked in an ontological and ontic malady. The artistic image is interpreted through an analogy that tries to resist a reifying, objectifying or mechanical relation with an artwork, and one that acknowledges its distinctness, differentness, separateness, and rends, and that accepts the threat of semiotic collapse and its incomprehensible kernel. The intellectual context that is addressed and disrupted at the same time is oriented around the writings on the image of the French philosopher Jean-Luc Nancy's (*1940), the existential and clinical term of a 'divided self', the subject of research in R. D. Laing's book, The Divided Self, published in 1960, and the thinking of a cultural ontology by the Romanian philosopher Constantin Noica's (1909-1987). [ABSTRACT FROM AUTHOR]

In Phenomenology of Perception (1945) Maurice Merleau-Ponty warns against considering depth and breadth as interchangeable. Rather than following Merleau-Ponty's thinking, this article considers the productive potential of equating depth with breadth, citing works by British painters Jane Harris, Beth Harland and John Wilkins. The tableau is proposed in this context as a holding apparatus, one that facilitates and contains a switch and shift between positions and dimensions. Holding is considered in three key ways: holding back, holding fast and holding attention, each one describing both the internal mechanisms of the tableau and its external relations with an observer. This holding characteristic is put forward as part of the constraints and potential of addressing a pictorial form, and connected to Michael Fried's writing, and the absorbed and diverted attention described by Jonathan Crary. George Berkeley's theories of vision are discussed via Merleau-Ponty, with breadth offered as a sideways version of depth, exposing the space between things and implying a repositioning of an observer to facilitate visibility. Although Meleau-Ponty outlines this exchangeability in order to discount it, this flexibility between one position and another, thinking oneself into a position rather than being there, is considered here as an active part of a pictorial practice, one that can inform a stand off between oppositional terms. [ABSTRACT FROM AUTHOR]

This article concerns the 'tableau photography' of the Canadian artist Jeff Wall (b. 1949), whose quotation from canonical paintings, especially of the nineteenth-century French painter Édouard Manet, has led interpreters to conclude that Wall is revitalizing Manet's peinture de la vie modern through the medium of photography. I propose, however, that the search for iconographical matches misses the real relationship between the two artists: a shared resistance to interpretation or 'illeg-ibility'. Wall's selection and manipulation of his sources blocks precisely the kind of interpretive work that ought to be enabled by identifying them, paradoxically illuminating an obscurity his work shares with them, which is obscured in turn by the very lucidity of the iconographical match. However, I argue that this illegibility is not equivalent to mere meaningless but is central to Wall's artistic enterprise, thereby restoring some substance to the cliché that Wall is a 'photographer of modern life'. [ABSTRACT FROM AUTHOR]

The article provides the background and context for the research papers published in this edition of the Journal. The Tate Modern conference, Tableau: Painting Photo Object, in 2011, expanded a problematic about the pictorial distinctions embedded in the concept of the tableau form, this discussion being most recently aired in the writings of Michael Fried and Jean-François Chevrier. The wider context links the tableau form to notions of dispositif and apparatus, terms that have become widely linked to the mechanisms and rhetoric of the modes of address of art forms. The research papers and the Tate conference have been part of the wider 'Tableau Project' whose aim is to open up discussion around historical, theoretical and contemporary practices that are linked to the tableau form. [ABSTRACT FROM AUTHOR]

Painting, read in relation to the tableau, is the subject of this article. A case is made against translating the tableau as 'picture form' or 'picture object'. Rather, leaving the term tableau untranslated seeks to recognize the dimensionality of the term as a temporal, conceptual, and compositional formation. The role of the tableau in the pictorial and theatrical arts is explored through reference to Roland Barthes' essay, 'Diderot, Brecht, Eisenstein'. The term reflects the necessary distillation, distanc-ing, cut, and composition that both disciplines share. For two contemporary painters, Christian Bonnefoi and Martin Barré, inherent in the concept of the tableau are operations of appearing, which counts on the invisible, of detachment, which counts on adherence, and discourse, which counts on a relation to 'objection' - all stemming from an insistence on the tableau's responsibility to address its limits. Consideration of the dispositif in the forming of the tableau recognizes the achievement of the tableau at the moment of the disappearance of the dispositif. [ABSTRACT FROM AUTHOR]

Abstract: When modelling realistic systems, physical constraints on the resources available are often required. For example, we might say that at most N processes can access a particular resource at any moment, exactly M participants are needed for an agreement, or an agent can be in exactly one mode at any moment. Such situations are concisely modelled where literals are constrained such that at most N, or exactly M, can hold at any moment in time. In this paper we consider a logic which is a combination of standard propositional linear time temporal logic with cardinality constraints restricting the numbers of literals that can be satisfied at any moment in time. We present the logic and show how to represent a number of case studies using this logic. We propose a tableau-like algorithm for checking the satisfiability of formulae in this logic, provide details of a prototype implementation and present experimental results using the prover. [Copyright &y& Elsevier]

This paper aims to conduct a systematic overview of green growth literature and reveal the evolution, hot topics, as well as future directions of this field. Given the dispersion of the existing related studies, the development and evolution process of green growth have yet to be comprehensively reviewed. The qualitative review cannot objectively and quantitatively screen out important keywords, possibly leading to bias. This study uses a hybrid method based on bibliometric analysis and the fuzzy Delphi method to review 806 papers from the Scopus database. The findings show that there is an exponential rise in publications with the leading authors, countries, and institutions concentrated in South Korea, China, and the USA. The contents of core literature are focused on pathways and influencing factors of green growth. Hot topics, including policy support, resource management, emission reduction, and the application of new technology, are summarized. The top 5 keywords for future directions are energy, economy, emission, development, and management. The findings offer some valuable contributions to both academic and practical investigations of green growth., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

This article claims that modern musical theatre began when dancers transformed the static tableaux of melodrama into episodes of singing and dancing. Though static, the melodramatic tableau had long been understood as suggesting incipient action; the musical distinguished itself generically by realizing this potential energy. The tableau vivant and the pose plastique had already laid the groundwork by deploying women's bodies to depict the melodramatic realm of ideality upon which melodrama focused. However, while melodrama valorized the arresting of a woman's body, the musical celebrated instead her performing power. It is precisely this use of women's bodies simultaneously as signifier of a mythic realm of melodramatic virtue and as eroticized yet empowered spectacle that creates the musical's affective disintegration. This genealogy demands that we reconsider the role of "The Black Crook" in theatre history, since it links the traditions of melodrama, posing entertainments, and musical theatre. [ABSTRACT FROM AUTHOR]

I provide a tableau system and completeness proof for a revised version of Carnap's semantics for quantified modal logic. For Carnap, a sentence is possible if it is true in some first order model. However, in a similar fashion to second order logic, no sound and complete proof theory can be provided for this semantics. This factor contributed to the ultimate disappearance of Carnapian modal logic from contemporary philosophical discussion. The proof theory I discuss comes close to Carnap's semantic vision and provides an interesting counterpoint to mainstream approaches to modal logic. Despite its historical origins, my intention is to demonstrate that this approach to modal logic is worthy of contemporary attention and that current debate is the poorer for its absence. [ABSTRACT FROM AUTHOR]

Abstract: Nested sequent systems for modal logics are a relatively recent development, within the general area known as deep reasoning. The idea of deep reasoning is to create systems within which one operates at lower levels in formulas than just those involving the main connective or operator. Prefixed tableaus go back to 1972, and are modal tableau systems with extra machinery to represent accessibility in a purely syntactic way. We show that modal nested sequents and prefixed modal tableaus are notational variants of each other, roughly in the same way that Gentzen sequent calculi and tableaus are notational variants. This immediately gives rise to new modal nested sequent systems which may be of independent interest. We discuss some of these, including those for some justification logics that include standard modal operators. [Copyright &y& Elsevier]

We present a sound, complete and implementable tableau method for deciding satisfiability of formulas in the propositional version of computation tree logic CTL*. This is the first such tableau. CTL* is an exceptionally important temporal logic with applications from hardware design to agent reasoning, but there is no easily automated reasoning approach to CTL*. The tableau here is a traditional tree-shaped or top-down style tableau, and affords the possibility of reasonably quick decisions on the satisfiability of medium-sized formulas and construction of small models for them. A straightforward subroutine is given for determining when looping allows successful branch termination, but much needed further development is left as future work. In particular, a more general repetition prevention mechanism is needed to speed up the task of tableau construction. [ABSTRACT FROM AUTHOR]

Healthcare workflows (careflows) involve complex, distributive processes with a high degree of variability. There are ubiquitous communication and enormous data and knowledge management requirements and the processes involve complex timing requirements, and are safety critical. Designing these processes and managing their performance is difficult and error-prone. Using verification techniques such as model checking, which are mathematical methods of proving correctness, we can reduce errors by ensuring that process designs satisfy their specifications. We describe a prototype next generation multithreaded model checker to reason about processes in careflows, sensitive to patient preferences and the goals of the careteam using a timed temporal logic extended with modalities of beliefs, desires, and intentions. Copyright © 2011 John Wiley & Sons, Ltd. We describe a prototype next generation multithreaded model checker to reason about healthcare workflows (careflows) using a timed temporal logic extended with modalities of beliefs, desires, and intentions. Our approach allows proving properties of careflows regarding patient safety and conformity to standards of care as well as being sensitive to patient preferences and the goals of the careteam. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions as examples, and give rise to a new poset that is analogous to Young''s lattice. We also introduce a new basis for the Hopf algebra of noncommutative symmetric functions NSym. This basis of NSym is dual to the basis of quasisymmetric Schur functions and its elements are the pre-image of the Schur functions under the forgetful map . We prove that the multiplicative structure constants of the noncommutative Schur functions, equivalently the coefficients of the skew quasisymmetric Schur functions when expanded in the quasisymmetric Schur basis, are nonnegative integers, satisfying a Littlewood–Richardson rule analogue that reduces to the classical Littlewood–Richardson rule under χ. As an application we show that the morphism of algebras from the algebra of Poirier–Reutenauer to Sym factors through NSym. We also extend the definition of Schur functions in noncommuting variables of Rosas–Sagan in the algebra NCSym to define quasisymmetric Schur functions in the algebra NCQSym. We prove these latter functions refine the former and their properties, and project onto quasisymmetric Schur functions under the forgetful map. Lastly, we show that by suitably labeling , skew quasisymmetric Schur functions arise in the theory of Pieri operators on posets. [Copyright &y& Elsevier]

Abstract: We present a decision procedure for hybrid logic equipped with nominals, the satisfaction operator and existential, difference, converse, reflexive, symmetric and transitive modalities. This decision procedure is a prefixed tableau method based on the one introduced by Bolander and Blackburn (2007) . It enhances its predecessor in terms of computational efficiency and handles more expressive logics. Its way of ensuring termination enables addition of rules for the difference modality, inspired by Kaminski and Smolka (2009) . [ABSTRACT FROM AUTHOR]

We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree of cyclotomic quotients of rings that categorify one-half of quantum sl( k). [ABSTRACT FROM AUTHOR]

The current recovery of the notion of landscape as a means of comprehending the relationships between nature, society and culture in their spatiotemporal dimensions, that is, as specific totalities, calls for a return to its most fecund presentations, beginning with what is perhaps the most outstanding version of them all, that of Alexander von Humboldt. On this occasion we intend to make a reading in terms of landscape of Essay on the Geography of Plants and of the accompanying Physical Tableau, the one of humboldtian works less known. We believe that our study will demonstrate that Humboldt's contribution on landscape and landscapes was to a great extent contained in the initial text of Geography of Plants; which in turn enables us to explore the fundamental relationship between landscape and the initial development of Biogeography. [ABSTRACT FROM AUTHOR]

Abstract: We prove a collection of conjectures of White [D. White, personal communication, 2007], as well as some related conjectures of Abuzzahab, Korson, Li, and Meyer [O. Abuzzahab, M. Korson, M. Li, S. Meyer, Cyclic and dihedral sieving for plane partitions, U. Minnesota REU Report, 2005] and of Reiner and White [V. Reiner, personal communication, 2007; D. White, personal communication, 2007], regarding the cyclic sieving phenomenon of Reiner, Stanton and White [V. Reiner, D. Stanton, D. White, The cyclic sieving phenomenon, J. Combin. Theory Ser. A 108 (2004)] as it applies to jeu-de-taquin promotion on rectangular tableaux. To do this, we use Kazhdan–Lusztig theory and a characterization of the dual canonical basis of due to Skandera [M. Skandera, On the dual canonical and Kazhdan–Lusztig bases and 3412, 4231-avoiding permutations, 2006, submitted for publication]. Afterwards, we extend our results to analyzing the fixed points of a dihedral action on rectangular tableaux generated by promotion and evacuation, suggesting a possible sieving phenomenon for dihedral groups. Finally, we give applications of this theory to cyclic sieving phenomena involving reduced words for the long elements of hyperoctohedral groups and noncrossing partitions. [Copyright &y& Elsevier]

The article considers an immanent, critical relation between theory and artistic practice and that this theoretical and critical background is not demonstrated by the work but in relation to painterly practice. It is literally a background to the making of the work where a series of propositions set up a critical dialogue. An important and recurrent theme discussed is the relationship between cultural hegemony and painterly abstraction in terms of questions of signification. [ABSTRACT FROM AUTHOR]

Abstract: Schützenberger’s theorem for the ordinary RSK correspondence naturally extends to Chen et al.’s correspondence for matchings and partitions. Thus the counting of bilaterally symmetric -noncrossing partitions naturally arises as an analogue for involutions. In obtaining the analogous result for 3-noncrossing partitions, we use a different technique to develop a Maple package for 2-dimensional vacillating lattice walk enumeration problems. The package also applies to the hesitating case. As applications, we find several interesting relations for some special bilaterally symmetric partitions. [Copyright &y& Elsevier]

This article focuses on the ways in which collective emotions were staged during the years of perestroika. In the late 1980s, many theatre people in Latvia tried to formulate their protest against the political regime. A number of productions attempted to evoke feelings that had been intentionally suppressed and even erased from public memory. It was not accidental that theatrical representations of historical events or urgent political processes frequently culminated in a tableau where the gestures of the characters visually summarized the emotions and ideas of the situation rendering national sentiment in visible signs. The article tries to answer two questions: to what extent the social reality and the dominating theatrical forms of the late 1980s fostered the use of a tableau, and how concrete examples could be assessed against this background. The source materials used for analysis are photographs of theatre performances staged by Valentīns Maculēvičs - one of the leading figures of the Latvian theatre in the late 1980s. [ABSTRACT FROM AUTHOR]

By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove that a component of the filled-in Julia set of any polynomial is a point if and only if its forward orbit contains no periodic critical components. It follows immediately that the Julia set of a polynomial is a Cantor set if and only if each critical component of the filled-in Julia set is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992. [ABSTRACT FROM AUTHOR]

This article deals with representations of one specific city, Århus, Denmark, especially its central district. The analysis is based on anthropological fieldwork conducted in Skåde Bakker and Fedet, two well-off neighborhoods. The overall purpose of the project is to study perceptions of space and the interaction of cultural, social, and spatial organizations, as seen from the point of view of people living in Skåde Bakker and Fedet. The focus is on the city dwellers’ representations of the central district of Århus with specific reference to the concept of transit space. When applied to various Århusian locations, this might highlight unforeseen meanings and paradoxes. [ABSTRACT FROM AUTHOR]

We present a sound, complete and relatively straightforward tableau method for deciding valid formulas in the propositional version of the bundled (or suffix and fusion closed) computation tree logic BCTL*. This proves that BCTL* is decidable. It is also moderately useful to have a tableau available for a reasonably expressive branchingtime temporal logic. However, the main interest in this should be that it leads us closer to being able to devise a tableau-based technique for theorem-proving in the important full computational tree logic CTL*. [ABSTRACT FROM AUTHOR]

Let F be a field, and α0,...,αk-1 be k distinct elements of F. Let λ =(λ1,...,λk) be a partition of n and V λ be the set of all vectors v=( v 1,..., v n)∈ F n such that |{ j ∈ [ n] : v j=αi}|=λi+1 for 0≦ i ≦\ k-1. We describe the lexicographic standard monomials of the ideal of polynomials from F[ x 1,..., x n] which vanish on the set V λ. In the proof we give a new description of the orthogonal complement ( S λ)⊥ (with respect to the James scalar product) of the Specht module S λ. As applications, a basis of ( S λ)⊥ is exhibited, and we obtain a combinatorial description of the Hilbert function of V λ.. Our approach gives also the deglex standard monomials of V λ, and hence provides a new proof of a result of A. M. Garsia and C. Procesi [10]. [ABSTRACT FROM AUTHOR]

La contemplation et la perception d'une œuvre d'art au complet implique le regard et l'orientation de la tête. Cette dernière dépend des informations proprioceptives du cou. L'application des vibrations sur les muscles du cou stimulent ces informations, et peut générer des réponses posturales. Nous voulons déterminer si l'application de vibrations nucales modifie l'exploration visuelle d'une œuvre d'art, et comment la tâche d'exploration affecte les réponses posturales aux vibrations. Vingt adultes en bonne santé porteront un système de suivi du regard (Tobii) et l'application App Balance de mesure de l'équilibre. En position debout, ils exploreront trois tableaux (largeur > 1 m) et identifieront 7 détails. L'exploration se fera sans ou avec vibrations nucales (gauches et droites) (VB115, TechnoConcept) de manière randomisée. Un test d'exploration visuelle de type papier-crayon (test des cloches) sera également effectué en position assise. Les tableau seront divisés en 7 colonnes ; la 1re colonne explorée, les temps de fixation et le nombre de visite sur chaque colonne, ainsi que l'activité posturale seront comparés entre les différentes conditions. L'application de vibrations nucales modifiera l'exploration visuelle. Les réponses posturales aux vibrations seront atténuées lors de l'exploration, du fait du meilleur ancrage visuel fourni par l'exploration. Les personnes avec des déficits de la perception visuelle pourraient bénéficier de ce type d'intervention, en situation écologique. Les données des sujets en bonne santé aideront à interpréter les résultats de ces patients recrutés dans une future étude. [ABSTRACT FROM AUTHOR]

Abstract: Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is . We present a stronger theorem with a purely combinatorial proof using the Robinson–Schensted correspondence and a new concept called chess tableaux. We also prove a sharpening of another conjecture by Stanley concerning weighted sums of squares of sign-imbalances. The proof is built on a remarkably simple relation between the sign of a permutation and the signs of its RS-corresponding tableaux. [Copyright &y& Elsevier]

In this paper, three refinements on I-SATCHMO are presented. I-SATCHMO is an application of the backjumping strategy for SATCHMO, which is a model generation theorem prover and is formalized as positive unit hyperresolution tableaux, to pruning away redundant branches. However, I-SATCHMO does not completely implement backjumping. Since marking an atom as useful whenever it contributes to a forward chaining reasoning, I-SATCHMO suffers from two problems. One is that the atoms that only contribute to irrelevant forward chaining reasoning are marked as ‘useful’. The other is that the atoms that are only useful for the sibling branches of the branch under consideration are taken as ‘useful’ for the branch. In both cases, I-SATCHMO might take some irrelevant violated clauses as ‘relevant’ and therefore use them to expand the search space. Moreover, not utilizing the partial reasoning results derivable during reasoning, I-SATCHMO might make repeated reasoning. Addressing these problems, our extension, called R-SATCHMO, refines I-SATCHMO in three ways: (1) only making the atoms that contribute to relevant forward chaining reasoning as useful; (2) it distinguishes between the set of useful atoms in different branches of a proof tree; (3) it summarizes the derived refutations as nogoods and utilizes them to avoid repeated reasoning. Hence, R-SATCHMO always searches a subspace of that which I-SATCHMO does. R-SATCHMO is optimal in the sense that during reasoning no same complete subtree is constructed in a proof tree. Moreover, R-SATCHMO can be used to generate minimal unsatisfiable subsets of an unsatisfiable set of clauses, and the strategies proposed in R-SATCHMO are applicable to minimal model generation procedures. We describe our refinements, present our implementation, prove the correctness, provide examples to demonstrate the power of our refinements, and discuss the application to minimal model generation. [ABSTRACT FROM PUBLISHER]

This paper presents a complete axiomatization for propositional interval temporal logic (PITL) with projection. The axiomatization is based on a tableau decision procedure for the logic, which in turn is founded upon a normal form for PITL formluae. The construction of the axiomatization provides a general mechanism for generating axiomatizations thus: given a normal form for a new connective, axioms can be generated for the connective from the tableau construction using that normal form. The paper concludes with a discussion of aspects of compositionality for PITL with projection. [ABSTRACT FROM PUBLISHER]

Answering a question of Kuniba, Misra, Okado, Takagi, and Uchiyama, it is shown that certain higher level Demazure characters of affine type A, coincide with the graded characters of coordinate rings of closures of conjugacy classes of nilpotent matrices. [ABSTRACT FROM AUTHOR]

Minimal Herbrand models of sets of first-order clauses are useful in several areas of computer science, for example, automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes an approach for generating the minimal Herbrand models of sets of first-order clauses. The approach builds upon positive unit hyperresolution ( PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depth-first relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MM-SATCHMO, of this procedure is given, and its performance on benchmark suites is reported. The second minimal model generation procedure performs a breadth-first, constrained expansion of PUHR (complement) tableaux. Both procedures are optimal in the sense that each minimal model is constructed only once, and the construction of nonminimal models is interrupted as soon as possible. They are complete in the following sense: The depth-first minimal model generation procedure computes all minimal Herbrand models of the considered clauses provided these models are all finite. The breadth-first minimal model generation procedure computes all finite minimal Herbrand models of the set of clauses under consideration. The proposed procedures are compared with related work in terms of both principles and performance on benchmark problems. [ABSTRACT FROM AUTHOR]

In this paper we show that the existence of plane partitions, which are minimal in a sense to be defined, yields minimal irreducible summands in the Kronecker product χλ ⊗ χμ of two irreducible characters of the symmetric group S(n). The minimality of the summands refers to the dominance order of partitions of n. The multiplicity of a minimal summand χν equals the number of pairs of Littlewood-Richardson multitableaux of shape (λ, μ), conjugate content and type ν. We also give lower and upper bounds for these numbers. [ABSTRACT FROM AUTHOR]