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Quantifiers in logic and proof-search using permissive-nominal terms and sets

M. J. Gabbay, C.-P. Wirth
2013 Journal of Logic and Computation  
The key innovation is the use of syntax and semantics with (finitely-supported) namesymmetry, in the style of nominal techniques.  ...  We investigate models of first-order logic designed to give semantics to reductive proofsearch systems, with special attention to the so-called γand δ-rules controlling quantifiers.  ...  This paper is about proof-search using nominal terms (which is not the same thing as nominal abstract syntax) with semantics in nominal sets.  ... 
doi:10.1093/logcom/exs057 fatcat:f5uh43hgxzay3fhj5oiat4f27u

Nominal abstraction

Andrew Gacek, Dale Miller, Gopalan Nadathur
2011 Information and Computation  
Higher-order abstract syntax λ-Tree syntax Proof search Reasoning about operational semantics Recursive relational specifications are commonly used to describe the computational structure of formal systems  ...  Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and  ...  Acknowledgments We are grateful to Alwen Tiu whose observations with respect to the earlier formulation of our ideas in terms of ∇quantifiers in the heads of clauses eventually led us to a recasting using  ... 
doi:10.1016/j.ic.2010.09.004 fatcat:xzgekcouqrdjbdbweyk5bdz674

Two-level nominal sets and semantic nominal terms: an extension of nominal set theory for handling meta-variables

MURDOCH J. GABBAY
2011 Mathematical Structures in Computer Science  
Nominal sets are a sets-based first-order denotation for variables in logic and programming. In this paper we extend nominal sets to two-level nominal sets.  ...  We discuss the connections between this and nominal terms and prove a soundness result.  ...  This generalisation includes nominal terms (Urban et al. 2004 ), permissive-nominal terms , and the syntax of predicates in permissive-nominal logic ).  ... 
doi:10.1017/s0960129511000272 fatcat:dmyixyrc7rd7xfn7oxxwbddofm

A two-level logic approach to reasoning about computations [article]

Andrew Gacek, Dale Miller, Gopalan Nadathur
2010 arXiv   pre-print
Associated with the specification logic are various notions of binding: for quantifiers within formulas, for eigenvariables within sequents, and for abstractions within terms.  ...  We provide these capabilities here by using a logic called G which represents relations over lambda-terms via definitions of atomic judgments, contains inference rules for induction and co-induction, and  ...  Reasoning over open terms is supported in the Nominal package via the nominal logic N-quantifier which has similarities to the ∇-quantifier.  ... 
arXiv:0911.2993v2 fatcat:k662fjb7jzdadaixy62l7jd7b4

A Two-Level Logic Approach to Reasoning About Computations

Andrew Gacek, Dale Miller, Gopalan Nadathur
2011 Journal of automated reasoning  
Associated with the specification logic are various notions of binding: for quantifiers within formulas, for eigenvariables within sequents, and for abstractions within terms.  ...  We provide these capabilities here by using a logic called G which represents relations over λ-terms via definitions of atomic judgments, contains inference rules for induction and co-induction, and includes  ...  Reasoning over open terms is supported in the Nominal package via the nominal logic N-quantifier which has similarities to the ∇-quantifier.  ... 
doi:10.1007/s10817-011-9218-1 fatcat:jtt7qft2jja25hpkr6ik4qemly

Logic Column 14: Nominal Logic and Abstract Syntax [article]

James Cheney
2005 arXiv   pre-print
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding  ...  After an overview of other approaches, we describe nominal abstract syntax and nominal logic, a logic for reasoning about nominal abstract syntax.  ...  The reason is that αProlog's proof search and unification techniques address only the equational theory of nominal logic.  ... 
arXiv:cs/0511025v1 fatcat:sro6jwwv65f2jnmxlzsulzr7r4

Nominal Abstraction [article]

Andrew Gacek, Dale Miller, Gopalan Nadathur
2010 arXiv   pre-print
Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such descriptions: the interpretation of atomic judgments through recursive definitions and  ...  We present examples to show that this logic can provide elegant treatments of binding contexts that appear in many proofs, such as those establishing properties of typing calculi and of arbitrarily cascading  ...  Acknowledgements We are grateful to Alwen Tiu whose observations with respect to the earlier formulation of our ideas in terms of ∇-quantifiers in the heads of clauses eventually led us to a recasting  ... 
arXiv:0908.1390v3 fatcat:q32rdms5tbdirgtdzvieq3tnie

Mechanized metatheory model-checking

James Cheney, Alberto Momigliano
2007 Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '07  
In this paper, we consider the problem of bounded model-checking for metatheoretic properties of formal systems specified using nominal logic.  ...  However, the dual problem of searching for errors in such formalizations has received comparatively little attention.  ...  This paper reflects only the authors' views and the Community is not liable for any use that may be made of the information contained therein.  ... 
doi:10.1145/1273920.1273931 dblp:conf/ppdp/CheneyM07 fatcat:igwzds3epvhp5e6m4wy65vksry

A Framework for Specifying, Prototyping, and Reasoning about Computational Systems [article]

Andrew Gacek
2009 arXiv   pre-print
and another logic that exploits the special characteristics of the specification logic to support reasoning about the computational behavior of systems that are described using it.  ...  Both logics embody a natural treatment of binding structure by using the lambda-calculus as a means for representing objects and by incorporating special mechanisms for working with such structure.  ...  Focusing and Proof Search Recent research has been looking at techniques for guiding proof search in G-like logics based on the notion of focusing [BM07, BMSV09a] .  ... 
arXiv:0910.0747v2 fatcat:lwdpd37pdvayjn73b2apt3okpa

Translating specifications from nominal logic to CIC with the theory of contexts

Marino Miculan, Ivan Scagnetto, Furio Honsell
2005 Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding - MERLIN '05  
We consider a natural-deduction style proof system for intuitionistic nominal logic, called NINL, inspired by a sequent proof system recently proposed by J. Cheney.  ...  We study the relation between Nominal Logic and the Theory of Contexts, two approaches for specifying and reasoning about datatypes with binders.  ...  Acknowledgements The authors wish to thank Pietro Di Gianantonio and the anonymous referees for their valuable suggestions.  ... 
doi:10.1145/1088454.1088460 dblp:conf/icfp/MiculanSH05 fatcat:trusxdzv6ra33p7fjt3skvyc74

Nominal logic programming

James Cheney, Christian Urban
2008 ACM Transactions on Programming Languages and Systems  
We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs.  ...  This article investigates logic programming based on nominal logic.  ...  His support for me and this work has been unyielding. My other committee members, Robert Constable and Geri Gay, have also been very supportive.  ... 
doi:10.1145/1387673.1387675 fatcat:longqgnr75aktkwdy56eeyu4ne

Schematic Polymorphism in the Abella Proof Assistant [article]

Gopalan Nadathur, Yuting Wang
2018 arXiv   pre-print
The proof structures that we consider for formulas that are schematized in this fashion are limited to ones whose type instances are valid proofs in the simply typed logic.  ...  Our ideas, which have been implemented in an updated version of the system, accommodate schematic polymorphism both in the core logic of Abella and in the executable specification logic that it embeds.  ...  Opinions, findings and conclusions or recommendations that are manifest in this material are those of the participants and do not necessarily reflect the views of the NSF.  ... 
arXiv:1806.07523v1 fatcat:ozrmkgjvbjfrveethoiveh3eie

Reasoning over Permissions Regions in Concurrent Separation Logic [chapter]

James Brotherston, Diana Costa, Aquinas Hobor, John Wickerson
2020 Lecture Notes in Computer Science  
nominal labels from hybrid logic.  ...  We contend that our suggested alterations bring formal reasoning with fractional permissions in separation logic considerably closer to common pen-and-paper intuition, while imposing only a modest bureaucratic  ...  of α, P holds"; it is definable using @ and an existential quantifier over labels.  ... 
doi:10.1007/978-3-030-53291-8_13 fatcat:h5kthdsmyrdchn2jymlvulnepi

The implementation of the Mezzo type-checker

Jonathan Protzenko
2014 Proceedings of the 25th symposium on Implementation and Application of Functional Languages - IFL '13  
In this paper, we formalize the core operations used for type-checking, and give corresponding algorithms. Two central operations, subtraction and merging, are detailed.  ...  We present the implementation of Mezzo, a programming language based on the notion of permission that provides strong guarantees about aliasing, ownership and mutable state.  ...  One may fully prove a program using a proof assistant, or rely on program logics embedded in Coq such as Ynot [15] or CFML [10] .  ... 
doi:10.1145/2620678.2620684 dblp:conf/ifl/Protzenko13 fatcat:yymeli5n2vhpxhregyvyv63aoe

Automated Situation-Aware Service Composition in Service-Oriented Computing

S.S. Yau, H. Davulcu, S. Mukhopadhyay, D. Huang, H. Gong, P. Singh, F. Gelgi
2007 International Journal of Web Services Research  
The authors would like to thank Ramesh Bharadwaj and James Kirby, Jr. of the U.S. Naval Research Laboratory for many helpful discussions.  ...  Our deductive proof system searches the state-space in a backward chaining manner using natural deduction and enforces constraints using the Enforce algorithm in a forward chaining manner.  ...  Conduct situation-aware service composition using the α-logic proof system and automated synthesis of situation-aware workflow agents described in α-calculus terms for runtime execution. 4.  ... 
doi:10.4018/jwsr.2007100103 fatcat:xdjafatqzzc43ahxhonjjxodsm
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