Relevant bibliographies by topics / Boolean valued models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Boolean valued models'

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Published: 1 February 2025

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Journal articles on the topic "Boolean valued models"

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Wu, Xinhe. "Boolean-Valued Models and Their Applications." Bulletin of Symbolic Logic 28, no. 4 (December 2022): 533. http://dx.doi.org/10.1017/bsl.2022.34.

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AbstractBoolean-valued models generalize classical two-valued models by allowing arbitrary complete Boolean algebras as value ranges. The goal of my dissertation is to study Boolean-valued models and explore their philosophical and mathematical applications.In Chapter 1, I build a robust theory of first-order Boolean-valued models that parallels the existing theory of two-valued models. I develop essential model-theoretic notions like “Boolean-valuation,” “diagram,” and “elementary diagram,” and prove a series of theorems on Boolean-valued models, including the (strengthened) Soundness and Completeness Theorem, the Löwenheim–Skolem Theorems, the Elementary Chain Theorem, and many more.Chapter 2 gives an example of a philosophical application of Boolean-valued models. I apply Boolean-valued models to the language of mereology to model indeterminacy in the parthood relation. I argue that Boolean-valued semantics is the best degree-theoretic semantics for the language of mereology. In particular, it trumps the well-known alternative—fuzzy-valued semantics. I also show that, contrary to what many have argued, indeterminacy in parthood entails neither indeterminacy in existence nor indeterminacy in identity, though being compatible with both.Chapter 3 (joint work with Bokai Yao) gives an example of a mathematical application of Boolean-valued models. Scott and Solovay famously used Boolean-valued models on set theory to obtain relative consistency results. In Chapter 3, I investigate two ways of extending the Scott–Solovay construction to set theory with urelements. I argue that the standard way of extending the construction faces a serious problem, and offer a new way that is free from the problem.Abstract prepared by Xinhe Wu.E-mail: xinhewu@mit.edu
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Dahn, Bernd I. "Boolean valued models and incomplete specifications." Journal of Logic Programming 12, no. 3 (February 1992): 225–36. http://dx.doi.org/10.1016/0743-1066(92)90025-x.

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OZAWA, MASANAO. "ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY." Review of Symbolic Logic 10, no. 4 (June 5, 2017): 782–807. http://dx.doi.org/10.1017/s1755020317000120.

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AbstractIn 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory.
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Hansen, Lars. "On an algebra of lattice-valued logic." Journal of Symbolic Logic 70, no. 1 (March 2005): 282–318. http://dx.doi.org/10.2178/jsl/1107298521.

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AbstractThe purpose of this paper is to present an algebraic generalization of the traditional two-valued logic. This involves introducing a theory of automorphism algebras, which is an algebraic theory of many-valued logic having a complete lattice as the set of truth values. Two generalizations of the two-valued case will be considered, viz., the finite chain and the Boolean lattice. In the case of the Boolean lattice, on choosing a designated lattice value, this algebra has binary retracts that have the usual axiomatic theory of the propositional calculus as suitable theory. This suitability applies to the Boolean algebra of formalized token models [2] where the truth values are, for example, vocabularies. Finally, as the actual motivation for this paper, we indicate how the theory of formalized token models [2] is an example of a many-valued predicate calculus.
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Hernandez, E. G. "Boolean-Valued Models of Set Theory with Automorphisms." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 32, no. 7-9 (1986): 117–30. http://dx.doi.org/10.1002/malq.19860320704.

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Dobrić, Vladimir, Pavle Milošević, Aleksandar Rakićević, Bratislav Petrović, and Ana Poledica. "Interpolative Boolean Networks." Complexity 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/2647164.

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Boolean networks are used for modeling and analysis of complex systems of interacting entities. Classical Boolean networks are binary and they are relevant for modeling systems with complex switch-like causal interactions. More descriptive power can be provided by the introduction of gradation in this model. If this is accomplished by using conventional fuzzy logics, the generalized model cannot secure the Boolean frame. Consequently, the validity of the model’s dynamics is not secured. The aim of this paper is to present the Boolean consistent generalization of Boolean networks, interpolative Boolean networks. The generalization is based on interpolative Boolean algebra, the [0,1]-valued realization of Boolean algebra. The proposed model is adaptive with respect to the nature of input variables and it offers greater descriptive power as compared with traditional models. For illustrative purposes, IBN is compared to the models based on existing real-valued approaches. Due to the complexity of the most systems to be analyzed and the characteristics of interpolative Boolean algebra, the software support is developed to provide graphical and numerical tools for complex system modeling and analysis.
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Butz, C., and I. Moerdijk. "An elementary definability theorem for first order logic." Journal of Symbolic Logic 64, no. 3 (September 1999): 1028–36. http://dx.doi.org/10.2307/2586617.

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In this paper, we will present a definability theorem for first order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us first observe that if M is a model of a theory T in a language , then, clearly, any definable subset S ⊂ M (i.e., a subset S = {a ∣ M ⊨ φ(a)} defined by some formula φ) is invariant under all automorphisms of M. The same is of course true for subsets of Mn defined by formulas with n free variables.Our theorem states that, if one allows Boolean valued models, the converse holds. More precisely, for any theory T we will construct a Boolean valued model M, in which precisely the T -provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a formula .Our presentation is entirely selfcontained, and only requires familiarity with the most elementary properties of model theory. In particular, we have added a first section in which we review the basic definitions concerning Boolean valued models.
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Molchanov, I. S. "Set-Valued Estimators for Mean Bodies Related to Boolean Models." Statistics 28, no. 1 (January 1996): 43–56. http://dx.doi.org/10.1080/02331889708802547.

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Trinh, Van-Giang, Belaid Benhamou, Thomas Henzinger, and Samuel Pastva. "Trap spaces of multi-valued networks: definition, computation, and applications." Bioinformatics 39, Supplement_1 (June 1, 2023): i513—i522. http://dx.doi.org/10.1093/bioinformatics/btad262.

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Abstract Motivation Boolean networks are simple but efficient mathematical formalism for modelling complex biological systems. However, having only two levels of activation is sometimes not enough to fully capture the dynamics of real-world biological systems. Hence, the need for multi-valued networks (MVNs), a generalization of Boolean networks. Despite the importance of MVNs for modelling biological systems, only limited progress has been made on developing theories, analysis methods, and tools that can support them. In particular, the recent use of trap spaces in Boolean networks made a great impact on the field of systems biology, but there has been no similar concept defined and studied for MVNs to date. Results In this work, we generalize the concept of trap spaces in Boolean networks to that in MVNs. We then develop the theory and the analysis methods for trap spaces in MVNs. In particular, we implement all proposed methods in a Python package called trapmvn. Not only showing the applicability of our approach via a realistic case study, we also evaluate the time efficiency of the method on a large collection of real-world models. The experimental results confirm the time efficiency, which we believe enables more accurate analysis on larger and more complex multi-valued models. Availability and implementation Source code and data are freely available at https://github.com/giang-trinh/trap-mvn.
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Pantle, Ursa, Volker Schmidt, and Evgueni Spodarev. "Central limit theorems for functionals of stationary germ-grain models." Advances in Applied Probability 38, no. 1 (March 2006): 76–94. http://dx.doi.org/10.1239/aap/1143936141.

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Conditions are derived for the asymptotic normality of a general class of vector-valued functionals of stationary Boolean models in the d-dimensional Euclidean space, where a Lindeberg-type central limit theorem for m-dependent random fields, m ∈ N, is applied. These functionals can be used to construct joint estimators for the vector of specific intrinsic volumes of the underlying Boolean model. Extensions to functionals of more general germ–grain models satisfying some mixing and integrability conditions are also discussed.
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Dissertations / Theses on the topic "Boolean valued models"

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Santiago, Suárez Juan Manuel. "Infinitary logics and forcing." Electronic Thesis or Diss., Université Paris Cité, 2024. http://www.theses.fr/2024UNIP7024.

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Les principaux résultats de cette thèse sont liés au forcing, mais notre présentation bénéficie de sa mise en relation avec un autre domaine de la logique: la théorie des modèles des logiques infinitaires. Une idée clé de notre travail, qui était plus ou moins implicite dans les recherches de nombreux auteurs, est que le forcing joue un rôle en logique infinitaire similaire à celui joué par le théorème de compacité en logique du premier ordre. Plus précisément, de la même manière que le théorème de compacité est l'outil clé pour produire des modèles de théories du premier ordre, le forcing peut être l'outil clé pour produire les modèles des théories infinitaires. La première partie de cette thèse explore la relation entre les logiques infinitaires et les modèles à valeurs booléennes. Une propriété de consistance est une famille d'ensembles de formules non contradictoires, fermée sous certaines opérations logiques naturelles. Les propriétés de consistance reproduisent dans le contexte des logiques infinitaires la technique donnée par la méthode de résolution pour produire des modèles d'une formule du premier ordre; elles sont l'outil standard pour produire des modèles de formules infinitaires non contradictoires. Le premier résultat majeur que nous établissons dans cette thèse est le Théorème d'Existence des Modèles Booléens, affirmant que toute formule dans un ensemble qui est dans une propriété de consistance possède un modèle à valeurs booléennes avec la propriété de "mixing", et renforce le résultat original de Mansfield. Le Théorème d'Existence des Modèles Booléens nous permet de prouver trois résultats supplémentaires dans la théorie des modèles des logiques infinitaires munis de la sémantique des modèles à valeurs booléennes avec la propriété de ``mixing": un théorème de complétude par rapport à un calcul de type Gentzen, un théorème d'interpolation et un théorème d'omission des types. Cependant, nous croyons que le résultat central de cette partie de la thèse est le Théorème de Compacité Conservative. Dans la poursuite d'une généralisation de la compacité du premier ordre pour les logiques infinitaires, nous introduisons le concept de "renforcement conservatif" et de "conservativité finie". Nous soutenons que la généralisation appropriée de la consistance finie (relative à la sémantique de Tarski pour la logique du premier ordre) est la conservativité finie (relative à la sémantique donnée par les modèles à valeurs booléennes). À notre avis, ces résultats nous permettent de soutenir que: Les modèles à valeurs booléennes avec la propriété de "mixing" fournissent une sémantique naturelle pour les logiques infinies. Dans la seconde partie de la thèse, nous nous appuyons sur les résultats de la première partie pour aborder la question suivante: pour quelle famille de formules infinitaires peut-on forcer l'existence d'un modèle de Tarski sans détruire les sous-ensembles stationnaires? Kasum et Velickovic ont introduit une caractérisation des formules pour lesquelles un modèle de Tarski peut être forcé par un forcing préservant les ensembles stationnaires (AS-goodness). Leur travail s'appuie sur le résultat révolutionnaire d'Asperò et Schindler. Nous définissons la propriété ASK - une variante de l'AS-goodness - que nous utilisons également de la même manière que Kasum et Velickovic. Il est démontré que pour toute formule ayant la propriété ASK, on peut forcer l'existence d'un modèle de Tarski d'une manière qui préserve les ensembles stationnaires. La preuve de ce résultat s'appuie sur la perspective de la théorie des modèles de forcing présentée dans la première partie de la thèse, tout en introduisant une nouvelle notion de forcing itéré. Cette présentation du forcing itéré est étroitement liée au Théorème de Compacité Conservateur, soulignant à nouveau l'analogie entre les paires (forcing, logiques infinitaires) et (compacité, logique du premier ordre)
The main results of this thesis are related to forcing, but our presentation benefits from relating them to another domain of logic: the model theory of infinitary logics. In the 1950s, after the basic framework of first-order model theory had been established, Carol Karp, followed by Makkai, Keisler and Mansfield among others, developed the area of logic known as "infinitary logics". One key idea from our work, which was more or less implicit in the research of many, is that forcing plays a role in infinitary logic similar to the role compactness plays in first-order logic. Specifically, much alike compactness is the key tool to produce models of first-order theories, forcing can be the key tool to produce the interesting models of infinitary theories. The first part of this thesis explores the relationship between infinitary logics and Boolean valued models. Leveraging on the translation of forcing in the Boolean valued models terminology, this part lays the foundations connecting infinitary logics to forcing. A consistency property is a family of sets of non-contradictory sentences closed under certain natural logical operations. Consistency properties are the standard tools to produce models of non-contradictory infinitary sentences. The first major result we establish in the thesis is the Boolean Model Existence Theorem, asserting that any sentence which belongs to some set which is in some consistency property has a Boolean valued model with the mixing property, and strengthens Mansfield's original result. The Boolean Model Existence Theorem allows us to prove three additional results in the model theory of Boolean valued models for the semantics induced by Boolean valued models with the mixing property: a completeness theorem, an interpolation theorem, and an omitting types theorem. These can be shown to be generalizations of the corresponding results for first order logic in view of the fact that a first order sentence has a Tarski model if and only if it has a Boolean valued model. However we believe that the central result of this part of the thesis is the Conservative Compactness Theorem. In pursuit of a generalization of first-order compactness for infinitary logics, we introduce the concepts of conservative strengthening and of finite conservativity. We argue that the appropriate generalization of finite consistency (relative to Tarski semantics for first order logic) is finite conservativity (relative to the semantics given by Boolean valued models). The Conservative Compactness Theorem states that any finitely conservative family of sentences admits a Boolean valued model with the mixing property. In our opinion these results support the claim: Boolean-valued models with the mixing property provide a natural semantics for infinitary logics. In the second part of the thesis we leverage on the results of the first part to address the following question: For what family of infinitary formulae can we force the existence of a Tarski model for them without destroying stationary sets? Kasum and Velickovic introduced a characterization of which sentences can be forced by a stationary set preserving forcing (AS-goodness). Their work builds on the groundbreaking result of Asperò and Schindler. We define the ASK property -a variant of AS-goodness- which we also employ to the same effect of Kasum and Velickovic. It is shown that for any formula with the ASK-property, one can force the existence of a Tarski model in a stationary set preserving way. The proof of this result builds on the model theoretic perspective of forcing presented in the first part of the thesis, and does so introducing a new notion of iterated forcing. This presentation of iterated forcing is strictly intertwined with the Conservative Compactness Theorem, thereby emphasizing again the analogy between the pairs (forcing, infinitary logics) and (compactness, first-order logic)
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Books on the topic "Boolean valued models"

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L, Bell J. Set theory: Boolean-valued models and independence proofs. 3rd ed. Oxford [Oxfordshire]: Clarendon Press, 2011.

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Bell, J. L. Boolean-valued models and independence proofs in set theory. 2nd ed. Oxford: Clarendon, 1985.

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Makkai, Mihály. Models, logics, and higher-dimensional categories: A tribute to the work of Mihaly Makkai. Providence, R.I: American Mathematical Society, 2011.

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Button, Tim, and Sean Walsh. Boolean-valued structures. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0013.

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Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.
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Bell, John L. Set Theory: Boolean-Valued Models and Independence Proofs. Oxford University Press, 2005.

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Bell, John L. Set Theory: Boolean-Valued Models and Independence Proofs. Ebsco Publishing, 2005.

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Boolean-valued models and independence proofs in set theory. 2nd ed. Oxford [Oxfordshire]: Oxford University Press, 1985.

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Simplified Independence Proofs: Boolean Valued Models of Set Theory. Elsevier Science & Technology Books, 2011.

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Bell, John L. Set Theory: Boolean-Valued Models and Independence Proofs (Oxford Logic Guides). Oxford University Press, USA, 2005.

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Geometric Set Theory. American Mathematical Society, 2020.

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Book chapters on the topic "Boolean valued models"

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Viale, Matteo. "Boolean Valued Models." In UNITEXT, 81–105. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-71660-7_6.

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Dahn, Bernd I. "Boolean valued models and incomplete specifications." In Algebraic and Logic Programming, 119–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/3-540-50667-5_63.

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Pierobon, Moreno, and Matteo Viale. "Boolean Valued Models, Sheafifications, and Boolean Ultrapowers of Tychonoff Spaces." In Chapman Mathematical Notes, 355–90. Cham: Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-68934-5_14.

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da Costa, N. C. A., and F. A. Doria. "Structures, Suppes Predicates, and Boolean-Valued Models in Physics." In Philosophical Logic and Logical Philosophy, 91–118. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8678-8_7.

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Eckert, Daniel, and Frederik Herzberg. "The Problem of Judgment Aggregation in the Framework of Boolean-Valued Models." In Lecture Notes in Computer Science, 138–47. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09764-0_9.

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Yang, Jiong, and Kuldeep S. Meel. "Rounding Meets Approximate Model Counting." In Computer Aided Verification, 132–62. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-37703-7_7.

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AbstractThe problem of model counting, also known as $$\#\textsf{SAT}$$ # SAT , is to compute the number of models or satisfying assignments of a given Boolean formula F. Model counting is a fundamental problem in computer science with a wide range of applications. In recent years, there has been a growing interest in using hashing-based techniques for approximate model counting that provide $$(\varepsilon , \delta )$$ ( ε , δ ) -guarantees: i.e., the count returned is within a $$(1+\varepsilon )$$ ( 1 + ε ) -factor of the exact count with confidence at least $$1-\delta $$ 1 - δ . While hashing-based techniques attain reasonable scalability for large enough values of $$\delta $$ δ , their scalability is severely impacted for smaller values of $$\delta $$ δ , thereby preventing their adoption in application domains that require estimates with high confidence.The primary contribution of this paper is to address the Achilles heel of hashing-based techniques: we propose a novel approach based on rounding that allows us to achieve a significant reduction in runtime for smaller values of $$\delta $$ δ . The resulting counter, called $$\textsf{ApproxMC6}$$ ApproxMC 6 (The resulting tool $$\textsf{ApproxMC6}$$ ApproxMC 6 is available open-source at https://github.com/meelgroup/approxmc), achieves a substantial runtime performance improvement over the current state-of-the-art counter, $$\textsf{ApproxMC}$$ ApproxMC . In particular, our extensive evaluation over a benchmark suite consisting of 1890 instances shows $$\textsf{ApproxMC6}$$ ApproxMC 6 solves 204 more instances than $$\textsf{ApproxMC}$$ ApproxMC , and achieves a $$4\times $$ 4 × speedup over $$\textsf{ApproxMC}$$ ApproxMC .
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Tan, Jianping, Kunpeng Han, Yao Liu, Xiaoxuan Huang, and Erte Lin. "Optimization of Damping Groove Parameters of Swashplate Plunger Pump Based on CATIA Secondary Development." In Lecture Notes in Mechanical Engineering, 925–39. Singapore: Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-7887-4_81.

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Abstract In order to improve the performance of the plunger pump, aiming at the problems of flow pulsation and pressure overshoot of the plunger pump, a new compound slot flow distribution buffer tank structure is proposed. CATIA modeling software is used to obtain the overflow area curve of the valve plate through Boolean operation. Through the secondary development of the software, the overflow area curve of the valve plate under different parameter values can be obtained efficiently. Then the pressure, flow and other related parameters of the pump can be observed in the AMESim model of the plunger pump. The results show that the flow pulsation and pressure overshoot can be effectively reduced when the depth Angle is 7°, the width Angle is 90° and the composite aperture is 0.8 mm.
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Damonte, Alessia. "Testing Joint Sufficiency Twice: Explanatory Qualitative Comparative Analysis." In Texts in Quantitative Political Analysis, 153–86. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-12982-7_7.

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AbstractStandard Qualitative Comparative Analysis (QCA) applies an eliminative cross-case algorithm to identify which combinations of factors are logically associated with an outcome in a population. As such, it suits the purpose of pinpointing the conditions under which an outcome occurs or fails. However, the explanatory import of its findings only follows if the algorithm identifies theoretically interpretable, logically valid, and empirically plausible causal compounds.The chapter provides an essential guide to designing an explanatory QCA that meets the three credibility requirements at once. Section 7.2 addresses how to develop starting hypotheses consistent with the assumptions of complex causation to preserve theoretical interpretability. Section 7.3 introduces the Boolean algebra required to model a hypothesis and find which part supports the explanatory claim in the cases at hand. Section 7.4 addresses the issue of gauging conditions to ensure the empirical plausibility of the analysis. Last, Sect. 7.5 summarizes the protocol, illustrated by the replicable example in the online R file.
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"Forcing and Boolean-valued models." In Multiple Forcing, 2–6. Cambridge University Press, 1987. http://dx.doi.org/10.1017/cbo9780511721168.002.

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Dahn, Bernd I. "BOOLEAN VALUED MODELS AND INCOMPLETE SPECIFICATIONS." In Algebraic and Logic Programming, 119–26. De Gruyter, 1988. http://dx.doi.org/10.1515/9783112620267-012.

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Conference papers on the topic "Boolean valued models"

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Figallo-Orellano, Aldo, and Juan Sebastián Slagter. "Models for da Costa’s paraconsistent set theory." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/wbl.2020.11456.

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In this work we will be constructed F-structures-valued models as generalization of Boolean-valued models and proved that these models that verify Leibniz’ Law validate all the set-theoretic axioms of da Costa’s Paraconsistent Set Theory type ZF.
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Shcherba, E. V. "Boolean-valued models of telecommunication systems in some problems of network security." In 2015 International Siberian Conference on Control and Communications (SIBCON). IEEE, 2015. http://dx.doi.org/10.1109/sibcon.2015.7147292.

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Liu, Han, Xiangnan He, Fuli Feng, Liqiang Nie, Rui Liu, and Hanwang Zhang. "Discrete Factorization Machines for Fast Feature-based Recommendation." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/479.

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User and item features of side information are crucial for accurate recommendation. However, the large number of feature dimensions, e.g., usually larger than 107, results in expensive storage and computational cost. This prohibits fast recommendation especially on mobile applications where the computational resource is very limited. In this paper, we develop a generic feature-based recommendation model, called Discrete Factorization Machine (DFM), for fast and accurate recommendation. DFM binarizes the real-valued model parameters (e.g., float32) of every feature embedding into binary codes (e.g., boolean), and thus supports efficient storage and fast user-item score computation. To avoid the severe quantization loss of the binarization, we propose a convergent updating rule that resolves the challenging discrete optimization of DFM. Through extensive experiments on two real-world datasets, we show that 1) DFM consistently outperforms state-of-the-art binarized recommendation models, and 2) DFM shows very competitive performance compared to its real-valued version (FM), demonstrating the minimized quantization loss.
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Kolb, Samuel, Martin Mladenov, Scott Sanner, Vaishak Belle, and Kristian Kersting. "Efficient Symbolic Integration for Probabilistic Inference." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/698.

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Weighted model integration (WMI) extends weighted model counting (WMC) to the integration of functions over mixed discrete-continuous probability spaces. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programs. Yet, state-of-the-art tools for WMI are generally limited either by the range of amenable theories, or in terms of performance. To address both limitations, we propose the use of extended algebraic decision diagrams (XADDs) as a compilation language for WMI. Aside from tackling typical WMI problems, XADDs also enable partial WMI yielding parametrized solutions. To overcome the main roadblock of XADDs -- the computational cost of integration -- we formulate a novel and powerful exact symbolic dynamic programming (SDP) algorithm that seamlessly handles Boolean, integer-valued and real variables, and is able to effectively cache partial computations, unlike its predecessor. Our empirical results demonstrate that these contributions can lead to a significant computational reduction over existing probabilistic inference algorithms.
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Bouskela, Daniel, Lena Buffoni, Audrey Jardin, Vince Molnair, Adrian Pop, and Armin Zavada. "The Common Requirement Modeling Language." In 15th International Modelica Conference 2023, Aachen, October 9-11. Linköping University Electronic Press, 2023. http://dx.doi.org/10.3384/ecp204497.

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CRML (the Common Requirement Modeling Language) is a new language for the formal expression of requirements. The ambition is to release the language as an open standard integrated into the open source modeling and simulation tool OpenModelica and interoperable with the open systems engineering standard SysMLv2. CRML allows to express requirements as multidisciplinary spatiotemporal constraints that can be verified against system design by co-simulating requirements models with behavioral models. Particular attention is paid to the following aspects. The requirements models must be easily legible and sharable between disciplines and stakeholders and must capture realistic constraints on the system, including time-dependent constraints with probabilistic criteria, in recognition of the fact that no constraint can be fulfilled at any time at any cost. The theoretical foundation of the language lies on 4-valued Boolean algebra, set theory and function theory. The coupling of the requirements models to the behavioral models is obtained through the specification of bindings, the automatic generation of Modelica code from the CRML model and use of the FMI and SSP standards. CRML and the proposed methodology is compatible with SysMLv2, forming a comprehensive work-flow and tool-chain encompassing requirement analysis, system design and V&V. The final objective is to facilitate the demonstration of correctness of system behavior against assumptions and requirements by building a workflow around Model-Driven Engineering and Open Standards for automating the creation of verification simulators.
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de Colnet, Alexis, and Stefan Mengel. "A Compilation of Succinctness Results for Arithmetic Circuits." In 18th International Conference on Principles of Knowledge Representation and Reasoning {KR-2021}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/kr.2021/20.

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Arithmetic circuits (AC) are circuits over the real numbers with 0/1-valued input variables whose gates compute the sum or the product of their inputs. Positive AC – that is, AC representing non-negative functions – subsume many interesting probabilistic models such as probabilistic sentential decision diagram (PSDD) or sum-product network (SPN) on indicator variables. Efficient algorithms for many operations useful in probabilistic reasoning on these models critically depend on imposing structural restrictions to the underlying AC. Generally, adding structural restrictions yields new tractable operations but increases the size of the AC. In this paper we study the relative succinctness of classes of AC with different combinations of common restrictions. Building on existing results for Boolean circuits, we derive an unconditional succinctness map for classes of monotone AC – that is, AC whose constant labels are non-negative reals – respecting relevant combinations of the restrictions we consider. We extend a small part of the map to classes of positive AC. Those are known to generally be exponentially more succinct than their monotone counterparts, but we observe here that for so-called deterministic circuits there is no difference between the monotone and the positive setting which allows us to lift some of our results. We end the paper with some insights on the relative succinctness of positive AC by showing exponential lower bounds on the representations of certain functions in positive AC respecting structured decomposability.
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Shcherba, E. V., and M. V. Shcherba. "Finding the Optimal Paths in a Boolean-Valued Network." In 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon). IEEE, 2019. http://dx.doi.org/10.1109/fareastcon.2019.8934413.

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Harder, Hans, Simon Jantsch, Christel Baier, and Clemens Dubslaff. "A Unifying Formal Approach to Importance Values in Boolean Functions." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/304.

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Boolean functions and their representation through logics, circuits, machine learning classifiers, or binary decision diagrams (BDDs) play a central role in the design and analysis of computing systems. Quantifying the relative impact of variables on the truth value by means of importance values can provide useful insights to steer system design and debugging. In this paper, we introduce a uniform framework for reasoning about such values, relying on a generic notion of importance value functions (IVFs). The class of IVFs is defined by axioms motivated from several notions of importance values introduced in the literature, including Ben-Or and Linial’s influence and Chockler, Halpern, and Kupferman’s notion of responsibility and blame. We establish a connection between IVFs and game-theoretic concepts such as Shapley and Banzhaf values, both of which measure the impact of players on outcomes in cooperative games. Exploiting BDD-based symbolic methods and projected model counting, we devise and evaluate practical computation schemes for IVFs.
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Yakhyaeva, Gulnara. "Application of Boolean Valued and Fuzzy Model Theory for Knowledge Base Development." In 2019 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON). IEEE, 2019. http://dx.doi.org/10.1109/sibircon48586.2019.8958245.

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Perhac, Jan, and Zuzana Bilanova. "Categorical Model of Functional Language with Natural Numbers and Boolean Values." In 2020 IEEE 15th International Conference on Computer Sciences and Information Technologies (CSIT). IEEE, 2020. http://dx.doi.org/10.1109/csit49958.2020.9322039.

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