Relevant bibliographies by topics / Higher order logics

Contents

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

Academic literature on the topic 'Higher order logics'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Higher order logics"

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Finkelstein, David. "Higher-order quantum logics." International Journal of Theoretical Physics 31, no. 9 (September 1992): 1627–38. http://dx.doi.org/10.1007/bf00671777.

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Hella, Lauri, and José M. Turull-Torres. "Expressibility of Higher Order Logics." Electronic Notes in Theoretical Computer Science 84 (September 2003): 129–40. http://dx.doi.org/10.1016/s1571-0661(04)80850-8.

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Aguirre, Alejandro, Gilles Barthe, Marco Gaboardi, Deepak Garg, Shin-ya Katsumata, and Tetsuya Sato. "Higher-order probabilistic adversarial computations: categorical semantics and program logics." Proceedings of the ACM on Programming Languages 5, ICFP (August 22, 2021): 1–30. http://dx.doi.org/10.1145/3473598.

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Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several domains, including security, privacy and machine learning. In this paper, we develop program logics for reasoning about adversarial computations in a higher-order setting. Our logics are built on top of a simply typed λ-calculus extended with a graded monad for probabilities and state. The grading is used to model and restrict the memory footprint and the cost (in terms of oracle calls) of computations. Under this view, an adversary is a higher-order expression that expects as arguments the code of its oracles. We develop unary program logics for reasoning about error probabilities and expected values, and a relational logic for reasoning about coupling-based properties. All logics feature rules for adversarial computations, and yield guarantees that are valid for all adversaries that satisfy a fixed resource policy. We prove the soundness of the logics in the category of quasi-Borel spaces, using a general notion of graded predicate liftings, and we use logical relations over graded predicate liftings to establish the soundness of proof rules for adversaries. We illustrate the working of our logics with simple but illustrative examples.
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Dal Lago, Ugo, Simone Martini, and Davide Sangiorgi. "Light Logics and Higher-Order Processes." Electronic Proceedings in Theoretical Computer Science 41 (November 28, 2010): 46–60. http://dx.doi.org/10.4204/eptcs.41.4.

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DAL LAGO, UGO, SIMONE MARTINI, and DAVIDE SANGIORGI. "Light logics and higher-order processes." Mathematical Structures in Computer Science 26, no. 6 (November 17, 2014): 969–92. http://dx.doi.org/10.1017/s0960129514000310.

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We show that the techniques for resource control that have been developed by the so-calledlight logicscan be fruitfully applied also to process algebras. In particular, we present a restriction of higher-order π-calculus inspired by soft linear logic. We prove that any soft process terminates in polynomial time. We argue that the class of soft processes may be naturally enlarged so that interesting processes are expressible, still maintaining the polynomial bound on executions.
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Hella, Lauri, and José María Turull-Torres. "Computing queries with higher-order logics." Theoretical Computer Science 355, no. 2 (April 2006): 197–214. http://dx.doi.org/10.1016/j.tcs.2006.01.009.

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Crary, Karl. "Higher-order representation of substructural logics." ACM SIGPLAN Notices 45, no. 9 (September 27, 2010): 131–42. http://dx.doi.org/10.1145/1932681.1863565.

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Benzmüller, Christoph, Dov Gabbay, Valerio Genovese, and Daniele Rispoli. "Embedding and automating conditional logics in classical higher-order logic." Annals of Mathematics and Artificial Intelligence 66, no. 1-4 (September 25, 2012): 257–71. http://dx.doi.org/10.1007/s10472-012-9320-z.

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Andrews, James H. "An untyped higher order logic with Y combinator." Journal of Symbolic Logic 72, no. 4 (December 2007): 1385–404. http://dx.doi.org/10.2178/jsl/1203350794.

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AbstractWe define a higher order logic which has only a notion of sort rather than a notion of type, and which permits all terms of the untyped lambda calculus and allows the use of the Y combinator in writing recursive predicates. The consistency of the logic is maintained by a distinction between use and mention, as in Gilmore's logics. We give a consistent model theory, a proof system which is sound with respect to the model theory, and a cut-elimination proof for the proof system. We also give examples showing what formulas can and cannot be used in the logic.
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Sági, Gábor. "A completeness theorem for higher order logics." Journal of Symbolic Logic 65, no. 2 (June 2000): 857–84. http://dx.doi.org/10.2307/2586575.

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AbstractHere we investigate the classes of representable directed cylindric algebras of dimension α introduced by Németi [12]. can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, “purely cylindric algebraic” proof for the following theorems of Németi: (i) is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain a strong representation theorem for if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories.
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Dissertations / Theses on the topic "Higher order logics"

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Assaf, Ali. "A framework for defining computational higher-order logics." Palaiseau, Ecole polytechnique, 2015. https://theses.hal.science/tel-01235303v4/document.

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The main aim of this thesis is to make formal proofs more universal by expressing them in a common logical framework. More specifically, we use the lambda-Pi-calculus modulo rewriting, a lambda calculus equipped with dependent types and term rewriting, as a language for defining logics and expressing proofs in those logics. By representing propositions as types and proofs as programs in this language, we design translations of various systems in a way that is efficient and that preserves their meaning. These translations can then be used for independent proof checking and proof interoperability. In this work, we focus on the translation of logics based on type theory that allow both computation and higher-order quantification as steps of reasoning. Pure type systems are a well-known example of such computational higher-order systems, and form the basis of many modern proof assistants. We design a translation of functional pure type systems to the lambda-Pi-calculus modulo rewriting based on previous work by Cousineau and Dowek. The translation preserves typing, and in particular it therefore also preserves computation. We show that the translation is adequate by proving that it is conservative with respect to the original systems. We also adapt the translation to support universe cumulativity, a feature that is present in modern systems such as intuitionistic type theory and the calculus of inductive constructions. We propose to use explicit coercions to handle the implicit subtyping that is present in cumulativity, bridging the gap between pure type systems and type theory with universes à la Tarski. We also show how to preserve the expressivity of the original systems by adding equations to guarantee that types have a unique term representation, thus maintaining the completeness of the translation. The results of this thesis have been applied in automated proof translation tools. We implemented programs that automatically translate the proofs of HOL, Coq, and Matita, to Dedukti, a type-checker for the lambda-Pi-calculus modulo rewriting. These proofs can then be re-checked and combined together to form new theories in Dedukti, which thus serves as an independent proof checker and a platform for proof interoperability. We tested our tools on a variety of libraries. Experimental results confirm that our translations are correct and that they are efficient compared to the state of the art.
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Freire, Cibele Matos. "Complexidade descritiva das lÃgicas de ordem superior com menor ponto fixo e anÃlise de expressividade de algumas lÃgicas modais." Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6359.

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Em Complexidade Descritiva investigamos o uso de logicas para caracterizar classes problemas pelo vies da complexidade. Desde 1974, quando Fagin provou que NP e capturado pela logica existencial de segunda-ordem, considerado o primeiro resultado da area, outras relac~oes entre logicas e classes de complexidade foram estabelecidas. Os resultados mais conhecidos normalmemte envolvem logica de primeira-ordem e suas extens~oes, e classes de complexidade polinomiais em tempo ou espaco. Alguns exemplos sÃo que a logica de primeira-ordem estendida com o operador de menor ponto xo captura a clsse P e que a logica de segunda-ordem estendida com o operador de fecho transitivo captura a classe PSPACE. Nesta dissertaÃÃo, analisaremos inicialmente a expressividade de algumas logicas modais com relacÃo ao problema de decisÃo REACH e veremos que e possvel expressa-lo com as logicas temporais CTL e CTL. Analisaremos tambem o uso combinado de logicas de ordem superior com o operador de menor ponto xo e obteremos como resultado que cada nvel dessa hierarquia captura cada nvel da hierarquia determinstica em tempo exponencial. Como corolario, provamos que a hierarquia de HOi(LFP) nÃo colapsa, ou seja, HOi(LFP) HOi+1(LFP)
In Descriptive Complexity, we investigate the use of logics to characterize computational classes os problems through complexity. Since 1974, when Fagin proved that the class NP is captured by existential second-order logic, considered the rst result in this area, other relations between logics and complexity classes have been established. Wellknown results usually involve rst-order logic and its extensions, and complexity classes in polynomial time or space. Some examples are that the rst-order logic extended by the least xed-point operator captures the class P and the second-order logic extended by the transitive closure operator captures the class PSPACE. In this dissertation, we will initially analyze the expressive power of some modal logics with respect to the decision problem REACH and see that is possible to express it with temporal logics CTL and CTL. We will also analyze the combined use of higher-order logics extended by the least xed-point operator and obtain as result that each level of this hierarchy captures each level of the deterministic exponential time hierarchy. As a corollary, we will prove that the hierarchy of HOi(LFP), for i 2, does not collapse, that is, HOi(LFP) HOi+1(LFP)
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TEICA, ELENA. "FORMAL CORRECTNESS AND COMPLETENESS FOR A SET OF UNINTERPRETED RTL TRANSFORMATIONS." University of Cincinnati / OhioLINK, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1001432470.

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Freire, Cibele Matos. "Complexidade descritiva das lógicas de ordem superior com menor ponto fixo e análise de expressividade de algumas lógicas modais." reponame:Repositório Institucional da UFC, 2010. http://www.repositorio.ufc.br/handle/riufc/17668.

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In Descriptive Complexity, we investigate the use of logics to characterize computational classes os problems through complexity. Since 1974, when Fagin proved that the class NP is captured by existential second-order logic, considered the rst result in this area, other relations between logics and complexity classes have been established. Wellknown results usually involve rst-order logic and its extensions, and complexity classes in polynomial time or space. Some examples are that the rst-order logic extended by the least xed-point operator captures the class P and the second-order logic extended by the transitive closure operator captures the class PSPACE. In this dissertation, we will initially analyze the expressive power of some modal logics with respect to the decision problem REACH and see that is possible to express it with temporal logics CTL and CTL . We will also analyze the combined use of higher-order logics extended by the least xed-point operator and obtain as result that each level of this hierarchy captures each level of the deterministic exponential time hierarchy. As a corollary, we will prove that the hierarchy of HOi(LFP), for i 2, does not collapse, that is, HOi(LFP) HOi+1(LFP)
Em Complexidade Descritiva investigamos o uso de logicas para caracterizar classes problemas pelo vies da complexidade. Desde 1974, quando Fagin provou que NP e capturado pela logica existencial de segunda-ordem, considerado o primeiro resultado da area, outras relac~oes entre logicas e classes de complexidade foram estabelecidas. Os resultados mais conhecidos normalmemte envolvem logica de primeira-ordem e suas extens~oes, e classes de complexidade polinomiais em tempo ou espaco. Alguns exemplos são que a l ogica de primeira-ordem estendida com o operador de menor ponto xo captura a clsse P e que a l ogica de segunda-ordem estendida com o operador de fecho transitivo captura a classe PSPACE. Nesta dissertação, analisaremos inicialmente a expressividade de algumas l ogicas modais com rela cão ao problema de decisão REACH e veremos que e poss vel express a-lo com as l ogicas temporais CTL e CTL . Analisaremos tamb em o uso combinado de l ogicas de ordem superior com o operador de menor ponto xo e obteremos como resultado que cada n vel dessa hierarquia captura cada n vel da hierarquia determin stica em tempo exponencial. Como corol ario, provamos que a hierarquia de HOi(LFP) não colapsa, ou seja, HOi(LFP) HOi+1(LFP)
FREIRE, Cibele Matos. Complexidade descritiva das lógicas de ordem superior com menor ponto fixo e análise de expressividade de algumas lógicas modais. 2010. 54 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Computação, Fortaleza-CE, 2010.
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Krishnaswami, Neelakantan R. "Verifying Higher-Order Imperative Programs with Higher-Order Separation Logic." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/164.

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In this thesis I show is that it is possible to give modular correctness proofs of interesting higher-order imperative programs using higher-order separation logic. To do this, I develop a model higher-order imperative programming language, and develop a program logic for it. I demonstrate the power of my program logic by verifying a series of examples. This includes both realistic patterns of higher-order imperative programming such as the subject-observer pattern, as well as examples demonstrating the use of higher-order logic to reason modularly about highly aliased data structures such as the union-find disjoint set algorithm.
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Zardini, Elia. "Living on the slippery slope : the nature, sources and logic of vagueness." Thesis, St Andrews, 2008. http://hdl.handle.net/10023/508.

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Nesi, Monica. "Formalising process calculi in higher order logic." Thesis, University of Cambridge, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627495.

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Camilleri, Albert John. "Executing behavioural definitions in Higher Order Logic." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.232795.

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Over the past few years, computer scientists have been using formal verification techniques to show the correctness of digital systems. The verification process, however, is complicated and expensive. Even proofs of simple circuits can involve thousands of logical steps. Often it can be extremely difficult to find correct device specifications and it is desirable that one sets off to prove a correct specification from the start, rather than repeatedly backtrack from the verification process to modify the original definitions after discovering they were incorrect or inaccurate. The main idea presented in the thesis is to amalgamate the techniques of simulation and verification, rather than have the latter replace the former. The result is that behavioural definitions can be simulated until one is reasonably sure that the specification is correct. Furthermore, providing the correctness with respect to these simulated specifications avoids the inadequacies of simulation, where it may not be computationally feasible to demonstrate correctness by exhaustive testing. Simulation here has a different purpose: to get specifications correct as early as possible in the verification process. Its purpose is not to demonstrate the correctness of the implementation - this is done in the verification stage when the very same specifications that were simulated are proven correct. The thesis discusses the implementation of an executable subset of the HOL logic, the version of Higher Order Logic embedded in the HOL theorem prover. It is shown that hardware can be effectively described using both relations and functions; relations being suitable for abstract specification, and functions being suitable for execution. The differences between relational and functional specifications are discussed and illustrated by the verification of an n-bit adder. Techniques for executing functional specifications are presented and various optimisation stratagies are shown which make the execution of the logic efficient. It is further shown that the process of generating optimised functional definitions from relational definitions can be automated. Example simulations of three hardware devices (a factorial machine, a small computer and a communications chip) are presented.
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Sultana, Nikolai. "Higher-order proof translation." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247345.

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The case for interfacing logic tools together has been made countless times in the literature, but it is still an important research question. There are various logics and respective tools for carrying out formal developments, but practitioners still lament the difficulty of reliably exchanging mathematical data between tools. Writing proof-translation tools is hard. The problem has both a theoretical side (to ensure that the translation is adequate) and a practical side (to ensure that the translation is feasible and usable). Moreover, the source and target proof formats might be less documented than desired (or even necessary), and this adds a dash of reverse-engineering to what should be a system integration task. This dissertation studies proof translation for higher-order logic. We will look at the qualitative benefits of locating the translation close to the source (where the proof is generated), the target (where the proof is consumed), and in between (as an independent tool from the proof producer and consumer). Two ideas are proposed to alleviate the difficulty of building proof translation tools. The first is a proof translation framework that is structured as a compiler. Its target is specified as an abstract machine, which captures the essential features of its implementations. This framework is designed to be performant and extensible. Second, we study proof transformations that convert refutation proofs from a broad class of consistency-preserving calculi (such as those used by many proof-finding tools) into proofs in validity-preserving calculi (the kind used by many proof-checking tools). The basic method is very simple, and involves applying a single transformation uniformly to all of the source calculi's inferences, rather than applying ad hoc (rule specific) inference interpretations.
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Fritz, Peter. "Intensional type theory for higher-order contingentism." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:b9415266-ad21-494a-9a78-17d2395eb8dd.

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Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is both contingent what individuals there are and contingent what propositions, properties and relations there are. I end up rejecting these views, and conclude that even if it is contingent what individuals there are, it is necessary what propositions, properties and relations there are. Call the view that it is contingent what individuals there are first-order contingentism, and the view that it is contingent what propositions, properties and relations there are higher-order contingentism. I bring together the three major contributions to the literature on higher-order contingentism, which have been developed largely independently of each other, by Kit Fine, Robert Stalnaker, and Timothy Williamson. I show that a version of Stalnaker's approach to higher-order contingentism was already explored in much more technical detail by Fine, and that it stands up well to the major challenges against higher-order contingentism posed by Williamson. I further show that once a mistake in Stalnaker's development is corrected, each of his models of contingently existing propositions corresponds to the propositional fragment of one of Fine's more general models of contingently existing propositions, properties and relations, and vice versa. I also show that Stalnaker's theory of contingently existing propositions is in tension with his own theory of counterfactuals, but not with one of the main competing theories, proposed by David Lewis. Finally, I connect higher-order contingentism to expressive power arguments against first-order contingentism. I argue that there are intelligible distinctions we draw with talk about "possible things", such as the claim that there are uncountably many possible stars. Since first-order contingentists hold that there are no possible stars apart from the actual stars, they face the challenge of paraphrasing such talk. I show that even in an infinitary higher-order modal logic, the claim that there are uncountably many possible stars can only be paraphrased if higher-order contingentism is false. I therefore conclude that even if first-order contingentism is true, higher-order contingentism is false.
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Books on the topic "Higher order logics"

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Paulson, Lawrence C. The representation of logics in higher-order logic. Cambridge: University of Cambridge, Computer Laboratory, 1987.

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Carreño, Victor A., César A. Muñoz, and Sofiène Tahar, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45685-6.

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Slind, Konrad, Annette Bunker, and Ganesh Gopalakrishnan, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/b100400.

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Mohamed, Otmane Ait, César Muñoz, and Sofiène Tahar, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71067-7.

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Basin, David, and Burkhart Wolff, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/b11935.

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Bertot, Yves, Gilles Dowek, Laurent Théry, André Hirschowitz, and Christine Paulin, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48256-3.

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Schneider, Klaus, and Jens Brandt, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-74591-4.

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Grundy, Jim, and Malcolm Newey, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0055125.

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Goos, Gerhard, Juris Hartmanis, Jan van Leeuwen, Joakim von Wright, Jim Grundy, and John Harrison, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0105392.

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Berghofer, Stefan, Tobias Nipkow, Christian Urban, and Makarius Wenzel, eds. Theorem Proving in Higher Order Logics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03359-9.

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Book chapters on the topic "Higher order logics"

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Kropf, Thomas. "Higher-Order Logics." In Introduction to Formal Hardware Verification, 207–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03809-3_5.

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Lu, Jianguo, Masateru Harao, and Masami Hagiya. "Higher Order Generalization." In Logics in Artificial Intelligence, 368–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/3-540-49545-2_25.

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Charalambidis, Angelos, Konstantinos Handjopoulos, Panos Rondogiannis, and William W. Wadge. "Extensional Higher-Order Logic Programming." In Logics in Artificial Intelligence, 91–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15675-5_10.

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Gordon, Michael J. C. "Mechanizing Programming Logics in Higher Order Logic." In Current Trends in Hardware Verification and Automated Theorem Proving, 387–439. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3658-0_10.

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Lescanne, Pierre. "Common Knowledge Logic in a Higher Order Proof Assistant." In Programming Logics, 271–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37651-1_11.

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Hella, Lauri, and José María Turull-Torres. "Complete Problems for Higher Order Logics." In Computer Science Logic, 380–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11874683_25.

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Turull-Torres, José Maria. "Relational Complexity and Higher Order Logics." In Lecture Notes in Computer Science, 311–33. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30024-5_17.

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Hintikka, Jaakko. "Standard vs. Nonstandard Logic: Higher-Order, Modal, and First-Order Logics." In Language, Truth and Logic in Mathematics, 130–43. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-2045-8_7.

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Hintermeier, Claus, Hélène Kirchner, and Peter D. Mosses. "R n - and G n -logics." In Higher-Order Algebra, Logic, and Term Rewriting, 90–108. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61254-8_21.

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Benzmüller, Christoph, and Bruno Woltzenlogel Paleo. "Higher-Order Modal Logics: Automation and Applications." In Reasoning Web. Web Logic Rules, 32–74. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21768-0_2.

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Conference papers on the topic "Higher order logics"

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Crary, Karl. "Higher-order representation of substructural logics." In the 15th ACM SIGPLAN international conference. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1863543.1863565.

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Maruyama, Yoshihiro. "Higher-Order Fuzzy Logics and their Categorical Semantics: Higher-Order Linear Completeness and Baaz Translation via Substructural Tripos Theory." In 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2021. http://dx.doi.org/10.1109/fuzz45933.2021.9494453.

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Benzmüller, Christoph. "A (Simplified) Supreme Being Necessarily Exists, says the Computer: Computationally Explored Variants of Gödel's Ontological Argument." In 17th International Conference on Principles of Knowledge Representation and Reasoning {KR-2020}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/kr.2020/80.

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An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt Gödel's modal ontological argument. Some argument premises are modified, others are dropped, modal collapse is avoided and validity is shown already in weak modal logics K and T. Key to the gained simplifications of Gödel's original theory is the exploitation of a link to the notions of filter and ultrafilter in topology. The paper illustrates how modern knowledge representation and reasoning technology for quantified non-classical logics can contribute new knowledge to other disciplines. The contributed material is also well suited to support teaching of non-trivial logic formalisms in classroom.
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Rose, Judy, and Samantha Low-Choy. "Modern Pedagogical Approaches to Teaching Mixed Methods to Social Science Researchers." In Fifth International Conference on Higher Education Advances. Valencia: Universitat Politècnica València, 2019. http://dx.doi.org/10.4995/head19.2019.9509.

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Mixed methods research is burgeoning across the social sciences. Yet there is a need to implement more modern approaches to teaching it in higher education. The aim of this work is to outline pedagogy and preliminary evaluation of new mixed methods workshops designed and implemented in an Australian university. A specific feature of these workshops included unpacking the ontological, epistemological and axiological understandings of various methods and the paradigms or worldviews that underpin each approach. This overview of the processes of scientific inquiry that permits mixing-in within and across quantitative and qualitative research designs aims to help participants to see how logics moved among these divides. In order to engage participants in critically learning about these abstract concepts, we adopted teaching strategies of flipped classroom and active learning. Results, from the workshop evaluations and individual learning reflections, provided preliminary evidence that: (i) due to this broad overview on mixed methods, participants would likely use mixed methods in the future in their field; and (ii) there is a strong appetite for high quality Mixed Methods instruction in higher education.
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Liu, Qiang, and Yongmei Liu. "Multi-agent Epistemic Planning with Common Knowledge." 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.2018/264.

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In the past decade, multi-agent epistemic planning has received much attention from both dynamic logic and planning communities. Common knowledge is an essential part of multi-agent modal logics, and plays an important role in coordination and interaction of multiple agents. However, existing implementations of multi-agent epistemic planning provide very limited support for common knowledge, basically static propositional common knowledge. Our work aims to extend an existing multi-agent epistemic planning framework based on higher-order belief change with the capability to deal with common knowledge. We propose a novel normal form for multi-agent KD45 logic with common knowledge. We propose satisfiability solving, revision and update algorithms for this normal form. Based on our algorithms, we implemented a multi-agent epistemic planner with common knowledge called MEPC. Our planner successfully generated solutions for several domains that demonstrate the typical usage of common knowledge.
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Schwering, Christoph. "A Reasoning System for a First-Order Logic of Limited Belief." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/173.

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Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning decidable or even tractable. While a number of such logics have been proposed in the past, they tend to remain for theoretical analysis only and their practical relevance is very limited. In this paper, we aim to go beyond the theory. Building on earlier work by Liu, Lakemeyer, and Levesque, we develop a logic of limited belief that is highly expressive but remains decidable in the first-order and tractable in the propositional case and exhibits some characteristics that make it attractive for an implementation. We introduce a reasoning system that employs this logic as representation language and present experimental results that showcase the benefit of limited belief.
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Charalambidis, Angelos, Panos Rondogiannis, and Antonis Troumpoukis. "Higher-order logic programming." In PPDP '16: 18th International Symposium on Principles and Practice of Declarative Programming. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2967973.2968607.

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Howe, Douglas J. "Higher-order abstract syntax in classical higher-order logic." In the Fourth International Workshop. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1577824.1577826.

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Li, Linna, and Wei Zhang. "Higher-Order Logic Recommender System." In 2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology. IEEE, 2008. http://dx.doi.org/10.1109/wiiat.2008.196.

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Qian, Zhenyu. "Higher-order equational logic programming." In the 21st ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/174675.177889.

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Reports on the topic "Higher order logics"

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Archer, Myla M., Ben L. DiVito, and Cesar Munoz. Proceedings STRATA 2003. First International Workshop on Design and Application of Strategies/Tactics in Higher Order Logics; Focus on PVS Experiences. Fort Belvoir, VA: Defense Technical Information Center, November 2003. http://dx.doi.org/10.21236/ada418902.

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Jindal, A., R. Overbeek, and W. McCune. A parallel processing approach for implementing high-performance first-order logic deduction systems. Office of Scientific and Technical Information (OSTI), April 1989. http://dx.doi.org/10.2172/6215473.

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