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Journal articles on the topic 'Stratified logic'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Przymusinska, Halina, and Teodor C. Przymusinski. "Weakly Stratified Logic Programs1." Fundamenta Informaticae 13, no. 1 (1990): 51–65. http://dx.doi.org/10.3233/fi-1990-13106.

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2

PRIOR, A. N. "Stratified Metric Tense Logic." Theoria 33, no. 1 (2008): 28–38. http://dx.doi.org/10.1111/j.1755-2567.1967.tb00607.x.

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3

Compton, Kevin J. "Stratified least fixpoint logic." Theoretical Computer Science 131, no. 1 (1994): 95–120. http://dx.doi.org/10.1016/0304-3975(94)90091-4.

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4

Fitting, Melvin, and Marion Ben-Jacob. "Stratified, Weak Stratified, and Three-Valued Semantics1." Fundamenta Informaticae 13, no. 1 (1990): 19–33. http://dx.doi.org/10.3233/fi-1990-13104.

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We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratifiable logic programs, producing a semantics we call weak stratified. Finally, we show weak stratified sem

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5

Pétry, A. "Stratified languages." Journal of Symbolic Logic 57, no. 4 (1992): 1366–76. http://dx.doi.org/10.2307/2275371.

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AbstractWe consider arbitrary stratified languages. We study structures which satisfy the same stratified sentences and we obtain an extension of Keisler's Isomorphism Theorem to this situation. Then we consider operations which are definable by a stratified formula and modify the ‘type’ of their argument by one; we prove that for such an operation F the sentence c = F(c) and the scheme φ(c) ↔ (F(c)), where ↔(x) varies among all the stratified formulas with no variable other than x free, imply the same stratified {c}-sentences.

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6

Grädel, Erich, and Gregory L. McColm. "Hierarchies in transitive closure logic, stratified Datalog and infinitary logic." Annals of Pure and Applied Logic 77, no. 2 (1996): 169–99. http://dx.doi.org/10.1016/0168-0072(95)00021-6.

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7

Baheri, Ali, and Peng Wei. "Multi-Fidelity Temporal Reasoning: A Stratified Logic for Cross-Scale System Specifications." Logics 3, no. 2 (2025): 5. https://doi.org/10.3390/logics3020005.

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We present Stratified Metric Temporal Logic (SMTL), a novel formalism for specifying and verifying the properties of complex cyber–physical systems that exhibit behaviors across multiple temporal and abstraction scales. SMTL extends existing temporal logics by incorporating a stratification operator, enabling the association of temporal properties with specific abstraction levels. This allows for the natural expression of multi-scale requirements while maintaining formal reasoning about inter-level relationships. We formalize the syntax and semantics of SMTL, proving that it strictly subsumes

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8

Kolaitis, Phokion G. "The expressive power of stratified logic programs." Information and Computation 90, no. 1 (1991): 50–66. http://dx.doi.org/10.1016/0890-5401(91)90059-b.

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9

Xu, Daoyun, and Decheng Ding. "FC-normal and extended stratified logic program." Science in China Series F Information Sciences 45, no. 4 (2002): 259–72. http://dx.doi.org/10.1360/02yf9023.

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10

Balbiani, Philippe. "A Modal Semantics of Negation in Logic Programming." Fundamenta Informaticae 16, no. 3-4 (1992): 231–62. http://dx.doi.org/10.3233/fi-1992-163-403.

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The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal comple

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11

Cantini, Andrea. "A fixed point theory over stratified truth." Mathematical Logic Quarterly 66, no. 4 (2020): 380–94. http://dx.doi.org/10.1002/malq.201900064.

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12

Forster, Thomas. "Permutations and stratified formulae a preservation theorem." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 36, no. 5 (1990): 385–88. http://dx.doi.org/10.1002/malq.19900360504.

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13

Rodabaugh, S. E. "Necessity of non-stratified and anti-stratified spaces in lattice-valued topology." Fuzzy Sets and Systems 161, no. 9 (2010): 1253–69. http://dx.doi.org/10.1016/j.fss.2009.11.010.

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14

Crabbé, Marcel. "The Hauptsatz for Stratified Comprehension: A Semantic Proof." Mathematical Logic Quarterly 40, no. 4 (1994): 481–89. http://dx.doi.org/10.1002/malq.19940400406.

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15

Baumgartner, Peter, and Elena Tartaglia. "Bottom-Up Stratified Probabilistic Logic Programming with Fusemate." Electronic Proceedings in Theoretical Computer Science 385 (August 29, 2023): 87–100. http://dx.doi.org/10.4204/eptcs.385.11.

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16

Nasso, Mauro Di. "Linearly Stratified Models for the Foundations of Nonstandard Mathematics." Mathematical Logic Quarterly 44, no. 1 (1998): 138–42. http://dx.doi.org/10.1002/malq.19980440111.

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17

Boffa, Maurice, and Paolo Casalegno. "The consistency of some 4-stratified subsystem of NF including NF3." Journal of Symbolic Logic 50, no. 2 (1985): 407–11. http://dx.doi.org/10.2307/2274229.

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As is well known, NF is a first-order theory whose language coincides with that of ZF. The nonlogical axioms of the theory are: Extensionality. (x)(y)[(z)(z ∈ x ↔ z ∈ y) → x = y].Comprehension. (Ex)(y)(y ∈ x ↔ ψ) for every stratified ψ in which x does not occur free (a formula of NF is said to be stratified if it can be turned into a formula of the simple theory of types by adding type indices (natural numbers ≥ 0) to its variables).Before stating our result, a few preliminaries are in order. Let T be the simple theory of types. If ψ is a formula of T, we denote by ψ+ the formula obtained from

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18

Ikemoto, Lisa C. "Egg freezing, stratified reproduction and the logic of not." Journal of Law and the Biosciences 2, no. 1 (2015): 112–17. http://dx.doi.org/10.1093/jlb/lsu037.

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19

Jäger, Gerhard, and Robert F. Stärk. "The defining power of stratified and hierarchical logic programs." Journal of Logic Programming 15, no. 1-2 (1993): 55–77. http://dx.doi.org/10.1016/0743-1066(93)90013-7.

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20

Benferhat, Salem, and Rania El Baida. "A stratified first order logic approach for access control." International Journal of Intelligent Systems 19, no. 9 (2004): 817–36. http://dx.doi.org/10.1002/int.20026.

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21

Fang, Jinming. "Stratified L-ordered quasiuniform limit spaces." Fuzzy Sets and Systems 227 (September 2013): 51–73. http://dx.doi.org/10.1016/j.fss.2013.04.007.

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22

Fang, Jinming, Kai Wang, and Qinghua Li. "Note on stratified L -ordered convergence structures." Fuzzy Sets and Systems 300 (October 2016): 147–51. http://dx.doi.org/10.1016/j.fss.2016.01.002.

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23

Hinnion, Roland. "Stratified and positive comprehension seen as superclass rules over ordinary set theory." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 36, no. 6 (1990): 519–34. http://dx.doi.org/10.1002/malq.19900360605.

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24

Baillot, Patrick. "Stratified coherence spaces: a denotational semantics for light linear logic." Theoretical Computer Science 318, no. 1-2 (2004): 29–55. http://dx.doi.org/10.1016/j.tcs.2003.10.015.

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25

Cabibbo, Luca. "The Expressive Power of Stratified Logic Programs with Value Invention." Information and Computation 147, no. 1 (1998): 22–56. http://dx.doi.org/10.1006/inco.1998.2734.

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26

Tupailo, Sergei. "Consistency of strictly impredicative NF and a little more …" Journal of Symbolic Logic 75, no. 4 (2010): 1326–38. http://dx.doi.org/10.2178/jsl/1286198149.

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AbstractAn instance of Stratified Comprehensionis called strictly impredicative iff, under minimal stratification, the type of x is 0. Using the technology of forcing, we prove that the fragment of NF based on strictly impredicative Stratified Comprehension is consistent. A crucial part in this proof, namely showing genericity of a certain symmetric filter, is due to Robert Solovay.As a bonus, our interpretation also satisfies some instances of Stratified Comprehension which are not strictly impredicative. For example, it verifies existence of Frege natural numbers.Apparently, this is a new su

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27

Gutiérrez García, J. "On stratified L-valued filters induced by -filters." Fuzzy Sets and Systems 157, no. 6 (2006): 813–19. http://dx.doi.org/10.1016/j.fss.2005.09.003.

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28

Yao, Wei. "On many-valued stratified L-fuzzy convergence spaces." Fuzzy Sets and Systems 159, no. 19 (2008): 2503–19. http://dx.doi.org/10.1016/j.fss.2008.03.003.

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29

Salmasian, Hojjat, David Rubins, and David W. Bates. "Using the Electronic Health Record User Context in Clinical Decision Support Criteria." Applied Clinical Informatics 13, no. 04 (2022): 910–15. http://dx.doi.org/10.1055/s-0042-1756426.

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Abstract Background Computerized clinical decision support (CDS) used in electronic health record systems (EHRs) has led to positive outcomes as well as unintended consequences, such as alert fatigue. Characteristics of the EHR session can be used to restrict CDS tools and increase their relevance, but implications of this approach are not rigorously studied. Objectives To assess the utility of using “login location” of EHR users—that is, the location they chose on the login screen—as a variable in the CDS logic. Methods We measured concordance between user's login location and the location of

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30

Apt, Krzysztof R., and Howard A. Blair. "Arithmetic Classification of Perfect Models of Stratified Programs." Fundamenta Informaticae 13, no. 1 (1990): 1–17. http://dx.doi.org/10.3233/fi-1990-13103.

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We study here the recursion theoretic complexity of the perfect (Herbrand) models of stratified logic programs. We show that these models lie arbitrarily high in the arithmetic hierarchy. As a byproduct we obtain a similar characterization of the recursion theoretic complexity of the set of consequences in a number of formalisms for non-monotonic reasoning. We show that under some circumstances this complexity can be brought down to recursive enumerability.

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31

Rondogiannis, P. "Stratified negation in temporal logic programming and the cycle-sum test." Theoretical Computer Science 254, no. 1-2 (2001): 663–76. http://dx.doi.org/10.1016/s0304-3975(00)00374-1.

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32

COSTANTINI, STEFANIA. "On the existence of stable models of non-stratified logic programs." Theory and Practice of Logic Programming 6, no. 1-2 (2006): 169–212. http://dx.doi.org/10.1017/s1471068405002589.

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In this paper we analyze the relationship between cyclic definitions and consistency in Gelfond-Lifschitz's answer sets semantics (originally defined as ‘stable model semantics’). This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is given a syntactic characterization. This condition may have a practical importance both for defining new algorithms for checking consistency and computing answer sets, and for improv

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33

Tena Cucala, David J., Przemysław A. Wałęga, Bernardo Cuenca Grau, and Egor Kostylev. "Stratified Negation in Datalog with Metric Temporal Operators." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (2021): 6488–95. http://dx.doi.org/10.1609/aaai.v35i7.16804.

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We extend DatalogMTL—Datalog with operators from metric temporal logic—by adding stratified negation as failure. The new language provides additional expressive power for representing and reasoning about temporal data and knowledge in a wide range of applications. We consider models over the rational timeline, study their properties, and establish the computational complexity of reasoning. We show that, as in negation-free DatalogMTL, fact entailment in our language is PSPACE-complete in data and EXPSPACE-complete in combined complexity. Thus, the extension with stratified negation does not le

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34

De-xue, Zhang. "The stratified canonical fuzzy topology on I(L) is uniformizable." Fuzzy Sets and Systems 54, no. 2 (1993): 225–27. http://dx.doi.org/10.1016/0165-0114(93)90280-u.

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35

Zhang, Aidong, and Wiktor Marek. "On the Classification and Existence of Structures in Default Logic1." Fundamenta Informaticae 13, no. 4 (1990): 485–99. http://dx.doi.org/10.3233/fi-1990-13406.

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We investigate possible belief sets of an agent reasoning with default rules. Besides of Reiter’s extensions which are based on a proof-theoretic paradigm (similar to Logic Programming), other structures for default theories, based on weaker or different methods of constructing belief sets are considered, in particular, weak extensions and minimal sets. The first of these concepts is known to be closely connected to autoepistemic expansions of Moore, the other to minimal stable autoepistemic theories containing the initial assumptions. We introduce the concept of stratifed collection of defaul

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36

Bowler, Nathan, and Thomas Forster. "Normal subgroups of infinite symmetric groups, with an application to stratified set theory." Journal of Symbolic Logic 74, no. 1 (2009): 17–26. http://dx.doi.org/10.2178/jsl/1231082300.

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It is generally known that infinite symmetric groups have few nontrivial normal subgroups (typically only the subgroups of bounded support) and none of small index. (We will explain later exactly what we mean by small). However the standard analysis relies heavily on the axiom of choice. By dint of a lot of combinatorics we have been able to dispense—largely—with the axiom of choice. Largely, but not entirely: our result is that if X is an infinite set with ∣X∣ = ∣X × X∣ then Symm(X) has no nontrivial normal subgroups of small index. Some condition like this is needed because of the work of Sa

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37

Sagonas, Konstantinos, and Terrance Swift. "An abstract machine for tabled execution of fixed-order stratified logic programs." ACM Transactions on Programming Languages and Systems 20, no. 3 (1998): 586–634. http://dx.doi.org/10.1145/291889.291897.

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38

Li, Sanjiang, and Maokang Luo. "A note on stratified L-real line and unit L-interval." Fuzzy Sets and Systems 147, no. 2 (2004): 327–32. http://dx.doi.org/10.1016/j.fss.2004.01.001.

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39

Kaye, Richard. "A generalization of Specker's theorem on typical ambiguity." Journal of Symbolic Logic 56, no. 2 (1991): 458–66. http://dx.doi.org/10.2307/2274693.

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AbstractWe generalize Specker's theorem on typical ambiguity, that NF and TST + Ambiguity have the same stratified consequences, to the subschemes Amb(Γ) of ambiguity restricted to classes of sentences Γ with certain natural closure conditions.

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40

Aiguier, Marc, and Isabelle Bloch. "Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning." Journal of Applied Non-Classical Logics 29, no. 4 (2019): 392–429. http://dx.doi.org/10.1080/11663081.2019.1668678.

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41

Qiao, Junsheng. "On the reflective and coreflective subcategory of stratified L-Čech closure spaces." Fuzzy Sets and Systems 390 (July 2020): 105–17. http://dx.doi.org/10.1016/j.fss.2019.09.008.

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42

Cerna, David M., and Andrew Cropper. "Generalisation through Negation and Predicate Invention." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 9 (2024): 10467–75. http://dx.doi.org/10.1609/aaai.v38i9.28915.

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The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention. Combining these two features allows an ILP system to generalise better by learning rules with universally quantified body-only variables. We implement our idea in NOPI, which can learn normal logic programs with predicate invention, including Datalog programs with stratified negation. Our experimental results on multiple domains show that our approach can imp

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43

Syed, Moin. "The Logic of Microaggressions Assumes a Racist Society." Perspectives on Psychological Science 16, no. 5 (2021): 926–31. http://dx.doi.org/10.1177/1745691621994263.

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This commentary draws attention to core assumptions about the nature of society that underlie the current debate on microaggressions. For proponents of microaggression research, the starting assumption is one of a racist society. That is, microaggressions have their source and power within an inequitable, racially stratified society. In contrast, critics of microaggressions begin with the assumption of an equitable society, or at least would not endorse the assumption of a racist society. These two different starting assumptions lead to dramatically different conclusions about the concept of m

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44

Fletcher, Peter. "Nonstandard set theory." Journal of Symbolic Logic 54, no. 3 (1989): 1000–1008. http://dx.doi.org/10.2307/2274759.

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AbstractNonstandard set theory is an attempt to generalise nonstandard analysis to cover the whole of classical mathematics. Existing versions (Nelson, Hrbáček, Kawai) are unsatisfactory in that the unlimited idealisation principle conflicts with the wish to have a full theory of external sets.I re-analyse the underlying requirements of nonstandard set theory and give a new formal system, stratified nonstandard set theory, which seems to meet them better than the other versions.

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45

RONDOGIANNIS, PANOS, and IOANNA SYMEONIDOU. "The intricacies of three-valued extensional semantics for higher-order logic programs." Theory and Practice of Logic Programming 17, no. 5-6 (2017): 974–91. http://dx.doi.org/10.1017/s1471068417000357.

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AbstractM. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's tech

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46

BOGAERTS, BART, ANGELOS CHARALAMBIDIS, GIANNOS CHATZIAGAPIS, BABIS KOSTOPOULOS, SAMUELE POLLACI, and PANOS RONDOGIANNIS. "The Stable Model Semantics for Higher-Order Logic Programming." Theory and Practice of Logic Programming 24, no. 4 (2024): 737–54. https://doi.org/10.1017/s1471068424000231.

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AbstractWe propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic formalisms. The proposed semantics generalizes the classical two-valued stable model semantics of Gelfond and Lifschitz as well as the three-valued one of Przymusinski, retaining their desirable properties. Due to the use of AFT, we also get for free alternative semantics for higher-order logic programs, namely supported model, Kripke-Kleene, and well-found

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47

Hamkins, Joel David, and Andy Lewis. "Infinite time Turing machines." Journal of Symbolic Logic 65, no. 2 (2000): 567–604. http://dx.doi.org/10.2307/2586556.

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AbstractWe extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. Every set. for example, is decidable by such machines, and the semi-decidable sets form a portion of the sets. Our oracle concept leads to a notion of relative computability for sets of reals and a rich degree structure, stratified by two natural jump operators.

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48

Forster, Thomas. "ZF + “Every set is the same size as a wellfounded set”." Journal of Symbolic Logic 68, no. 1 (2003): 1–4. http://dx.doi.org/10.2178/jsl/1045861502.

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AbstractLet ZFB be ZF + “every set is the same size as a wellfounded set”. Then the following are true.Every sentence true in every (Rieger-Bernays) permutation model of a model of ZF is a theorem of ZFB. (i.e., ZFB is the theory of Rieger-Bernays permutation models of models of ZF) ZF and ZFAFA are both extensions of ZFB conservative for stratified formulæ. The class of models of ZFB is closed under creation of Rieger-Bernays permutation models.

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49

Apter, Arthur W., and Joel David Hamkins. "Indestructibility and the level-by-level agreement between strong compactness and supercompactness." Journal of Symbolic Logic 67, no. 2 (2002): 820–40. http://dx.doi.org/10.2178/jsl/1190150111.

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AbstractCan a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets. or less level-by-level agreement, such as requiring it only on measure one sets, then yes. it can.

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50

Wulansari, Harvini. "Uji Akurasi Klasifikasi Penggunaan Lahan dengan Menggunakan Metode Defuzzifikasi Maximum Likelihood Berbasis Citra Alos Avnir-2." BHUMI: Jurnal Agraria dan Pertanahan 3, no. 1 (2017): 98. http://dx.doi.org/10.31292/jb.v3i1.96.

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Land use information plays an important role in spatial planning and monitoring development in order to optimize landuse and to minimize land conflict. Remote sensing technology can be used to derive land cover information for land use information. The aim of this research was to study the accuracy level and the efficiency of fuzzy logic for land use classification. Defuzzification method was implemented using maximum likelihood and its landuse map from classification result, using spectral data from ALOS AVNIR-2. This research used fuzzy logic approach with defuzzification method using maximu

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