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Academic literature on the topic 'Order-sorted theories'

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Published: 11 March 2023

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Journal articles on the topic "Order-sorted theories"

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Lucas, Salvador, and Raúl Gutiérrez. "Automatic Synthesis of Logical Models for Order-Sorted First-Order Theories." Journal of Automated Reasoning 60, no. 4 (July 12, 2017): 465–501. http://dx.doi.org/10.1007/s10817-017-9419-3.

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Alpuente, María, Angel Cuenca-Ortega, Santiago Escobar, and José Meseguer. "Order-sorted Homeomorphic Embedding Modulo Combinations of Associativity and/or Commutativity Axioms*." Fundamenta Informaticae 177, no. 3-4 (December 10, 2020): 297–329. http://dx.doi.org/10.3233/fi-2020-1991.

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The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context of order-sorted rewrite theories that support symbolic execution methods modulo equational axioms. This paper generalizes the symbolic homeomorphic embedding relation to order–sorted rewrite theories that may contain various combinations of associativity and/or commutativity axioms for different binary operators. We systematically measure the performance of different, increasingly efficient formulations of the homeomorphic embedding relation modulo axioms that we implement in Maude. Our experimental results show that the most efficient version indeed pays off in practice.
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Lucas, Salvador. "Synthesis of models for order-sorted first-order theories using linear algebra and constraint solving." Electronic Proceedings in Theoretical Computer Science 200 (December 19, 2015): 32–47. http://dx.doi.org/10.4204/eptcs.200.3.

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Durán, Francisco, and José Meseguer. "On the Church-Rosser and coherence properties of conditional order-sorted rewrite theories." Journal of Logic and Algebraic Programming 81, no. 7-8 (October 2012): 816–50. http://dx.doi.org/10.1016/j.jlap.2011.12.004.

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LIU, Fu-Chun. "Lawvere Theorem in Institution of Regular Order-Sorted Equational Logic and Initial (Terminal) Semantics for Its Glued Theories." Journal of Software 16, no. 7 (2005): 1205. http://dx.doi.org/10.1360/jos161205.

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Decker, Valerie D., Philip D. Suman, Barb J. Burge, Ankita Deka, Melanie Harris, Dwight J. Hymans, Michael Marcussen, Donna Pittman, David Wilkerson, and James G. Daley. "Analysis of Social Work Theory Progression Published in 2004." Advances in Social Work 8, no. 1 (April 30, 2007): 81–103. http://dx.doi.org/10.18060/133.

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The authors reviewed 67 articles that discussed and/or tested human behavior theories from social work journals published in 2004 in order to assess the level and quality of theory progression. The articles were further sorted into Council on Social Work Education (CSWE) Educational Policy and Accreditation Standards (EPAS) Foundation Curriculum content areas of HBSE, practice, policy, field education, values & ethics, diversity, populations-at-risk/social and economic justice, and research for purposes of categorization. Results indicated that HBSE and practice were by far the largest group of articles reviewed.Also found was that social work has a limited amount of theory discussion in the content areas of field, values and ethics, diversity, and populations-at-risk/social and economic justice. Thirty-three articles were found to demonstrate theory progression, eight articles presented new/emerging theories, and 26 articles discussed or critiqued theories without presenting evidence of theory progression.
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Krajíček, Jan. "Discretely ordered modules as a first-order extension of the cutting planes proof system." Journal of Symbolic Logic 63, no. 4 (December 1998): 1582–96. http://dx.doi.org/10.2307/2586668.

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AbstractWe define a first-order extension LK(CP) of the cutting planes proof system CP as the first-order sequent calculus LK whose atomic formulas are CP-inequalities ∑i ai · xi ≥ b (xi's variables, ai's and b constants). We prove an interpolation theorem for LK(CP) yielding as a corollary a conditional lower bound for LK(CP)-proofs. For a subsystem R(CP) of LK(CP), essentially resolution working with clauses formed by CP-inequalities, we prove a monotone interpolation theorem obtaining thus an unconditional lower bound (depending on the maximum size of coefficients in proofs and on the maximum number of CP-inequalities in clauses). We also give an interpolation theorem for polynomial calculus working with sparse polynomials.The proof relies on a universal interpolation theorem for semantic derivations [16, Theorem 5.1].LK(CP) can be viewed as a two-sorted first-order theory of Z considered itself as a discretely ordered Z-module. One sort of variables are module elements, another sort are scalars. The quantification is allowed only over the former sort. We shall give a construction of a theory LK(M) for any discretely ordered module M (e.g., LK(Z) extends LK(CP)). The interpolation theorem generalizes to these theories obtained from discretely ordered Z-modules. We shall also discuss a connection to quantifier elimination for such theories.We formulate a communication complexity problem whose (suitable) solution would allow to improve the monotone interpolation theorem and the lower bound for R(CP).
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ALPUENTE, M., S. ESCOBAR, J. SAPIÑA, and A. CUENCA-ORTEGA. "Inspecting Maude variants withGLINTS." Theory and Practice of Logic Programming 17, no. 5-6 (August 24, 2017): 689–707. http://dx.doi.org/10.1017/s147106841700031x.

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AbstractThis paper introducesGLINTS, a graphical tool for exploring variant narrowing computations in Maude. The most recent version of Maude, version 2.7.1, provides quite sophisticated unification features, including order-sorted equational unification for convergent theories modulo axioms such as associativity, commutativity, and identity. This novel equational unification relies on built-in generation of the set ofvariantsof a termt, i.e., the canonical form oftσ for a computed substitution σ. Variant generation relies on a novel narrowing strategy calledfolding variant narrowingthat opens up new applications in formal reasoning, theorem proving, testing, protocol analysis, and model checking, especially when the theory satisfies thefinite variant property, i.e., there is a finite number of most general variants for every term in the theory. However, variant narrowing computations can be extremely involved and are simply presented in text format by Maude, often being too heavy to be debugged or even understood. TheGLINTSsystem provides support for (i) determining whether a given theory satisfies the finite variant property, (ii) thoroughly exploring variant narrowing computations, (iii) automatic checking of nodeembeddingandclosednessmodulo axioms, and (iv) querying and inspecting selected parts of the variant trees.
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DIACONESCU, RĂZVAN, and ALEXANDRE MADEIRA. "Encoding hybridized institutions into first-order logic." Mathematical Structures in Computer Science 26, no. 5 (November 12, 2014): 745–88. http://dx.doi.org/10.1017/s0960129514000383.

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A ‘hybridization’ of a logic, referred to as the base logic, consists of developing the characteristic features of hybrid logic on top of the respective base logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds). By ‘hybridized institutions’ we mean the result of this process when logics are treated abstractly as institutions (in the sense of the institution theory of Goguen and Burstall). This work develops encodings of hybridized institutions into (many-sorted) first-order logic (abbreviated $\mathcal{FOL}$) as a ‘hybridization’ process of abstract encodings of institutions into $\mathcal{FOL}$, which may be seen as an abstraction of the well-known standard translation of modal logic into $\mathcal{FOL}$. The concept of encoding employed by our work is that of comorphism from institution theory, which is a rather comprehensive concept of encoding as it features encodings both of the syntax and of the semantics of logics/institutions. Moreover, we consider the so-called theoroidal version of comorphisms that encode signatures to theories, a feature that accommodates a wide range of concrete applications. Our theory is also general enough to accommodate various constraints on the possible worlds semantics as well a wide variety of quantifications. We also provide pragmatic sufficient conditions for the conservativity of the encodings to be preserved through the hybridization process, which provides the possibility to shift a formal verification process from the hybridized institution to $\mathcal{FOL}$.
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Wang, Qingsong, Hongkun Xiao, Qiao Ma, Xueliang Yuan, Jian Zuo, Jian Zhang, Shuguang Wang, and Mansen Wang. "Review of Emergy Analysis and Life Cycle Assessment: Coupling Development Perspective." Sustainability 12, no. 1 (January 2, 2020): 367. http://dx.doi.org/10.3390/su12010367.

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Two methods of natural ecosystem assessment—emergy analysis (EMA) and life cycle assessment (LCA)—are reviewed in this paper. Their advantages, disadvantages, and application areas are summarized, and the similarities and differences between these two evaluation methods are analyzed respectively. Their research progress is also sorted out. The study finds that EMA and LCA share common attributes in evaluation processes and research fields, but they focus on different aspects of macrocosms and microcosms. The assessment of system sustainability is valued by both EMA and LCA, but the former has unique advantages in natural system input analysis, and the latter is more convincing in assessing environmental loading capacity. If the system boundaries of the two methods are expanded, in other words, factors such as ecosystem services, labor, and infrastructure construction are integrated into the upstream of the target system, and environmental impact is further analyzed using LCA in the downstream of the system, the two approaches would complete each other. The quantified results would be more objective. Therefore, these two theories have the necessity of coupling development. After reviewing recent coupling application cases, the results show that LCA and EMA have commonality in the upstream of the target system (mainly in inventory database construction), while the environmental impact assessment methods are different in the downstream. So the overall coupling analysis method is not formed. The current paper gives rational suggestions on the coupling development of the two systems in terms of the aggregate emergy flow table, the indicator system construction and indicator evaluation methods. In addition, it is necessary to introduce sensitivity analysis and uncertainty analysis in order to improve the reliability of assessment results. At present, the research on the coupling development of the two theories is in rapid development stage, but there are still many problems that need further exploration.
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Books on the topic "Order-sorted theories"

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Bell, John L. Categorical Logic and Model Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0007.

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The chapter begins with an introduction describing the development of categorical logic from the 1960s. The next section, `Categories and Deductive Systems’, describes the relationship between categories and propositional logic, while the ensuing section, `Functorial Semantics’, is devoted to Lawvere’s provision of the first-order theory of models with a categorical formulation. In the section `Local Set Theories and Toposes’ the categorical counterparts—toposes—to higher-order logic are introduced, along with their associated theories—local set theories. In the section `Models of First-Order Languages in Categories’ the idea of an interpretation of a many-sorted first-order language is introduced, along with the concept of generic model of a theory formulated in such a language. The chapter concludes with the section `Models in Toposes’, wherein is introduced the concept of a first-order geometric theory and its associated classifying topos containing a generic model of the theory.
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Book chapters on the topic "Order-sorted theories"

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Stell, John G. "Unique-sort order-sorted theories : A description as monad morphisms." In Conditional and Typed Rewriting Systems, 389–400. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54317-1_107.

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Lucas, Salvador, and José Meseguer. "Strong and Weak Operational Termination of Order-Sorted Rewrite Theories." In Rewriting Logic and Its Applications, 178–94. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12904-4_10.

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Durán, Francisco, and José Meseguer. "A Maude Coherence Checker Tool for Conditional Order-Sorted Rewrite Theories." In Rewriting Logic and Its Applications, 86–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16310-4_7.

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