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Permissive-nominal logic

Gilles Dowek, Murdoch J. Gabbay
2010 Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10  
Permissive-Nominal Logic (PNL) is an extension of firstorder logic where term-formers can bind names in their arguments.  ...  Like first-and higher-order logic and unlike other nominal logics, equality reasoning is not necessary to α-rename.  ...  Permissive-nominal logic can do this too, and because of its 'nominal' ancestry it does so in the style of nominal techniques.  ... 
doi:10.1145/1836089.1836111 dblp:conf/ppdp/DowekG10 fatcat:v4fdwmz2zjgcpivynpvoq3sckq

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.  ...  For surveys of the applications of permissive-nominal terms and nominal sets to logic and specification in general, see two survey papers [Gab11a, Gab12b] .  ... 
doi:10.1093/logcom/exs057 fatcat:f5uh43hgxzay3fhj5oiat4f27u

Permissive nominal terms and their unification: an infinite, co-infinite approach to nominal techniques

Gilles Dowek, Murdoch J. Gabbay, Dominic P. Mulligan
2010 Logic Journal of the IGPL  
Definitions of nominal and permissive nominal terms will follow. Nominal terms have been explored in logic-programming [7], rewriting [10], logic [19, 21], and elsewhere.  ...  We prove that expressivity is not lost moving to the permissive case and provide an injection of nominal terms unification problems and their solutions into permissive nominal terms problems and their  ...  Future work We propose permissive nominal terms as a syntax for designing logics and λ-calculi in the spirit of nominal terms. 45 A first implementation of permissive nominal unification has been made  ... 
doi:10.1093/jigpal/jzq006 fatcat:z44woxiotzfnjnpn46pjwtsdqu

Unity in nominal equational reasoning: The algebra of equality on nominal sets

Murdoch J. Gabbay
2012 Journal of Applied Logic  
There are currently no fewer than four dedicated logics for equality reasoning over nominal sets: nominal algebra, nominal equational logic, nominal equational logic with equality only, and permissive-nominal  ...  In this survey and research paper we present these logics side-by-side in a common notation, survey their similarities and differences, discuss their proof-and model-theories, and discuss in detail what  ...  , then permissive-nominal algebra and nominal equational logic with equality only (also permissive-nominal logic, which adds quantifiers [DG10, DG12] ).  ... 
doi:10.1016/j.jal.2012.03.001 fatcat:5vlldh6ssja4ne3bsrd63opevm

Nominal Terms and Nominal Logics: From Foundations to Meta-mathematics [chapter]

Murdoch J. Gabbay
2013 Handbook of Philosophical Logic  
These include: the nominal unification algorithm; nominal rewriting and its confluence proofs; nominal algebra, its soundness, completeness, and an HSP theorem; permissive-nominal logic and its soundness  ...  logic.  ...  equivalent in Permissive-Nominal Logic.  ... 
doi:10.1007/978-94-007-6600-6_2 fatcat:wpzfdpe6gnfvxjyfpfigthcwre

Finite and infinite support in nominal algebra and logic: nominal completeness theorems for free

Murdoch J. Gabbay
2012 Journal of Symbolic Logic (JSL)  
In conclusion, we consider different permissive-nominal syntaxes and nominal models and discuss how they relate to the results proved here.  ...  By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support.  ...  Permissive-nominal logic Permissive-nominal logic (PNL) extends signatures with proposition-formers P with arity α. It is 'first-order logic over (permissive-)nominal terms'.  ... 
doi:10.2178/jsl/1344862164 fatcat:ye3243gu45ez7awasyq4zgbor4

Universal algebra over lambda-terms and nominal terms

Murdoch J. Gabbay, Dominic P. Mulligan
2009 Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages Theory and Practice - LFMTP '09  
We use universal algebra, the logic of equational reasoning, a logical foundation based on an equality judgement form which is spartan but which is sufficiently expressive to encode mathematics in theory  ...  Both syntaxes involve name-abstraction: λ-terms represent functional abstraction; nominal terms represent atomsabstraction in nominal sets.  ...  Algebra-with-binding: nominal algebra and λ-theories Permissive nominal algebra We define permissive nominal terms (Definition 7).  ... 
doi:10.1145/1577824.1577835 dblp:conf/lfmtp/GabbayM09 fatcat:qmhgxjk2nvh3bgqoaw7gqvy444

PNL to HOL: From the logic of nominal sets to the logic of higher-order functions

Gilles Dowek, Murdoch J. Gabbay
2012 Theoretical Computer Science  
Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets.  ...  Then we have higher-order logic (HOL) and its models in ordinary (i.e. Zermelo-Fraenkel) sets; the denotation of forall or lambda is functions on full or partial function spaces.  ...  Permissive-nominal logic Permissive-nominal logic is a first-order logic for nominal terms quotiented by α-equivalence.  ... 
doi:10.1016/j.tcs.2012.06.007 fatcat:lviyhwpbrzg3vatztoffk26ady

Page 7664 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
, strict total orders, and transitive trees; nominal Until logic; and referential interval logic.  ...  Adding nominals to tense logic leads for several frame-classes to an increase in complexity of the satisfiability problem from PSPACE to EXPTIME.  ... 

Modeling Normative Multi-Agent Systems from a Kelsenian Perspective [article]

Christiano Braga, Edward Hermann Haeusler, Jéssica S. Santos
2018 arXiv   pre-print
Standard Deontic Logic (SDL) has been used as the underlying logic to model and reason over Multi-Agent Systems governed by norms (NorMAS).  ...  Due to the autonomy of the software agents of a NorMAS, norms may be violated and the underlying logic used to model the NorMAS should be able to represent violation scenarios.  ...  In Hybrid Logic terminology, norms are understood as nominals.  ... 
arXiv:1709.02018v2 fatcat:gxrmnbbe5bertjkxjqvs3ojog4

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.  ...  Semantic nominal terms have informed the design of permissive-nominal logic . The syntax of permissive-nominal logic is roughly equivalent to the implementation from Section 6.  ... 
doi:10.1017/s0960129511000272 fatcat:dmyixyrc7rd7xfn7oxxwbddofm

Reasoning over Permissions Regions in Concurrent Separation Logic [chapter]

James Brotherston, Diana Costa, Aquinas Hobor, John Wickerson
2020 Lecture Notes in Computer Science  
We propose an extension of separation logic with fractional permissions, aimed at reasoning about concurrent programs that share arbitrary regions or data structures in memory.  ...  labels from hybrid logic.  ...  We introduce nominals, or labels, from hybrid logic, where a nominal α is interpreted as denoting a unique heap.  ... 
doi:10.1007/978-3-030-53291-8_13 fatcat:h5kthdsmyrdchn2jymlvulnepi

Dynamic Delegation Based on Temporal Context

Ouarda Bettaz, Narhimene Boustia, Aicha Mokhtari
2016 Procedia Computer Science  
The description logic that we use for the re-formalization process is T-JClassic .  ...  This logic gives the mean to specify nonmonotonic authorizations, and a better representation of the temporal aspects specific to a given delegation.  ...  Permission (Alice, Consult, James-Patient-Records, Nominal).  ... 
doi:10.1016/j.procs.2016.08.137 fatcat:phk4wxcaszeb3ezfpczuswn25y

On How Kelsenian Jurisprudence and Intuitionistic Logic help to avoid Contrary-to-Duty paradoxes in Legal Ontologies [article]

Edward Hermann Haeusler, Alexandre Rademaker
2018 arXiv   pre-print
In this article we show how Hans Kelsen jurisprudence and Intuitionistic logic are used to avoid the well-known contrary-to-duty (CTD) paradoxes, such as Chisholm paradoxes and its variants.  ...  This article uses an intuitionistic version of the ALC description logic, named iALC, to show how an ontology based on individually valid legal statements is able to avoid CTDs by providing models to them  ...  The free choice permission paradox reported on (Ross, 1941) ) is derived on the supposition that there is a logic of norms, as for example SDL.  ... 
arXiv:1803.07543v1 fatcat:dablin2kijeo3pc6c2eufwo4h4

Page 302 of Automation and Remote Control Vol. 33, Issue 2 [page]

1972 Automation and Remote Control  
sequence with arbitrary permissible load.  ...  A noise signal may arise in a coupling line between elements, due to induction from external or internal sources, as a result of deviation from the nominal values of the parameters of preceding elements  ... 
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