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A Probabilistic Higher-order Fixpoint Logic [PDF]
Logical Methods in Computer Science, 2021 We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more expressive than
Yo Mitani +2 more
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The Complexity of Model Checking Higher-Order Fixpoint Logic [PDF]
Logical Methods in Computer Science, 2007 Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of programs that ...
Roland Axelsson +2 more
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Indexed linear logic and higher-order model checking [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 In recent work, Kobayashi observed that the acceptance by an alternating tree automaton A of an infinite tree T generated by a higher-order recursion scheme G may be formulated as the typability of the recursion scheme G in an appropriate intersection ...
Charles Grellois, Paul-André Melliès
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Equivalence of two Fixed-Point Semantics for Definitional Higher-Order Logic Programs [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point construction defined on
Angelos Charalambidis +2 more
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Language and Proofs for Higher-Order SMT (Work in Progress) [PDF]
Electronic Proceedings in Theoretical Computer Science, 2017 Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories.
Haniel Barbosa +4 more
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A relational logic for higher-order programs [PDF]
Proceedings of the ACM on Programming Languages, 2017 Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for reasoning about a broad range of properties, including equivalence and refinement, and specialized notions such ...
ALEJANDRO AGUIRRE +4 more
openaire +6 more sources
Systematic Verification of the Modal Logic Cube in Isabelle/HOL [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without restriction to the
Christoph Benzmüller +2 more
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First steps in synthetic guarded domain theory: step-indexing in the topos of trees [PDF]
Logical Methods in Computer Science, 2012 We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms,
Lars Birkedal +3 more
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Superposition for Lambda-Free Higher-Order Logic [PDF]
Logical Methods in Computer Science, 2021 We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables.
Alexander Bentkamp +3 more
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The Frege-Geach Problem and the Logic of Higher-Order Attitudes [PDF]
Pizhūhish/hā-yi Falsafī- Kalāmī, 2023 Moral expressivism suggests that 1) moral sentences lack truth conditions and 2) our purpose in asserting moral sentences is to express non-cognitive attitudes such as desires, approval, or disapproval.
Bahram Alizade
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