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Nominal logic programming

James Cheney, Christian Urban
2008 ACM Transactions on Programming Languages and Systems  
This article investigates logic programming based on nominal logic.  ...  We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs.  ...  The subject of this dissertation is nominal logic programming, that is, logic programming with nominal abstract syntax.  ... 
doi:10.1145/1387673.1387675 fatcat:longqgnr75aktkwdy56eeyu4ne

Completeness and incompleteness in nominal Kleene algebra

Dexter Kozen, Konstantinos Mamouras, Alexandra Silva
2017 Journal of Logical and Algebraic Methods in Programming  
Gabbay and Ciancia (2011) presented a nominal extension of Kleene algebra as a framework for trace semantics with dynamic allocation of resources, along with a semantics consisting of nominal languages  ...  They also provided an axiomatization that captures the behavior of the scoping operator and its interaction with the Kleene algebra operators and proved soundness over nominal languages.  ...  Regular expressions are normally interpreted as regular sets of strings, but there are other useful interpretations: binary relation models used in programming language semantics, the (min, +) algebra  ... 
doi:10.1016/j.jlamp.2017.06.002 fatcat:r3zc5bsmpzhhhogbewmmxny5ne

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.  ...  Nominal logic The two best-known 'nominal' logics are probably the nominal logic of [28] and FM set theory. Both are Hilbert-style theories -sets of axioms -in first-order logic.  ... 
doi:10.1145/1836089.1836111 dblp:conf/ppdp/DowekG10 fatcat:v4fdwmz2zjgcpivynpvoq3sckq

Composition-nominative logics of free-quantifier levels
Композиційно-номінативні логіки безкванторних рівнів

S.S. Shkilniak, Kiev Taras Shevchenko National University, D.B. Volkovytskyi, Kiev Taras Shevchenko National University
Free-quantifier composition nominative logics of partial quasiary predicates are considered.  ...  Languages and semantic models of such logics are described, their semantic properties are studied, in particular the properties of relations of logical consequence.  ... 
doi:10.15407/pp2016.02-03.038 fatcat:fx7ynnf7h5antj73h3dfiwszuu

First-order composition-nominative logics with predicates of weak equality and of strong equality
Першопорядковi композиційно-номінативні логіки з предикатами слабкої та строгої рівності

S.S. Shkilniak, Kiev Taras Shevchenko National University
Досліджено нові програмно-орієнтовані логіки часткових предикатів з операцією (композицією) предикатного доповнення, такі логіки названо LC. Для першопорядкових LC запропоновано низку відношень логічного наслідку та відношень логічного наслідку за умови невизначеності. Досліджено властивості цих відношень, встановлено співвідношення між ними. Для відношень типів |= T та |= F доведено теорему про елімінацію умов невизначеності. Для запропонованих відношень описано умови їх гарантованої
more » ... наведено властивості декомпозиції формул та елімінації кванторів. Ключові слова: логіка, частковий предикат, композиційна алгебра, логічний наслідок.
doi:10.15407/pp2019.03.028 fatcat:62hhvt5d3rdnhlq76d5klf4dvy

Composition nominative modal logics of partial non-monotone predicates and their calculi
Композиційно-номінативні модальні логіки немонотонних часткових предикатів та їх числення

O.S. Shkilniak, Kiev Taras Shevchenko National University, V.S. Kasianiuk, L.M. Malutenko, Kiev Taras Shevchenko National University, Kiev Taras Shevchenko National University
Досліджено нові програмно-орієнтовані логічні формалізми модального типу -композиційнономінативні модальні логіки немонотонних часткових предикатів. Описано семантичні моделі та мови цих логік, розглянуто основні семантичні властивості. Введено відношення наслідку для формул у стані, описано властивості відношення логічного наслідку для множин специфікованих станами формул. На цій основі для загальних i темпоральних модальних логік немонотонних предикатів побудовано числення секвенційного типу.
more » ... Описано різновиди цих числень, для них доведено теореми к оректності й повноти. Ключові слова: модальна логіка, частковий предикат, логічний наслідок, секвенційне числення.
doi:10.15407/pp2017.02.024 fatcat:3kbufkxu65aqlk4qzx4lvore3a

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 study the relation between Nominal Logic and the Theory of Contexts, two approaches for specifying and reasoning about datatypes with binders.  ...  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.  ...  Nominal signatures in Nominal Logic Given a nominal signature S, we can readily define a nominal logic for reasoning about its properties.  ... 
doi:10.1145/1088454.1088460 dblp:conf/icfp/MiculanSH05 fatcat:trusxdzv6ra33p7fjt3skvyc74

Composition-Nominative Logics as Institutions

Alexey Chentsov, Mykola Nikitchenko
2018 Logica Universalis  
Composition-nominative logics (CNL) are program-oriented logics. They are based on algebras of partial predicates which do not have fixed arity.  ...  Relations with institutions for classical first-order logic are considered. Directions for further investigation are outlined.  ...  Introduction Composition-nominative logics (CNL) are program-oriented algebra-based logics.  ... 
doi:10.1007/s11787-018-0191-x fatcat:wdpdr5f76rfh5cki656u2ztw64

Semantics-based Logics over Hierarchical Nominative Data

Mykola S. Nikitchenko, Stepan S. Shkilniak
2012 International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications  
Semantic properties of these logics are studied; corresponding sequent calculi are defined, their soundness and completeness are proved for logics of renominative level.  ...  In the paper new logics oriented on hierarchical data are developed. Algebras of partial predicates over such data with special compositions as operations form a semantic base for constructed logics.  ...  Here we give a short characteristic only to composition-nominative pure predicate logics; predicate-function logics are described in [3] ; as to composition-nominative program logics some initial variants  ... 
dblp:conf/icteri/NikitchenkoS12 fatcat:lgxqn6fizzcrhigxbnwmv2k3a4

Satisfiability in composition-nominative logics

Mykola Nikitchenko, Valentyn Tymofieiev
2012 Open Computer Science  
AbstractComposition-nominative logics are algebra-based logics of partial predicates constructed in a semantic-syntactic style on the methodological basis, which is common with programming.  ...  In this paper we present and investigate algorithms for solving the satisfiability problem in various classes of composition-nominative logics.  ...  form a kernel of program semantics structures. • Nominativity principle: nominative (naming) relations are basic ones in constructing data and programs.  ... 
doi:10.2478/s13537-012-0027-3 fatcat:qy4kya66tjhb7m4wlb7alqswou

Implementation of the Composition-nominative Approach to Program Formalization in Mizar

Ievgen Ivanov, Artur Kornilowicz, Mykola Nikitchenko
2018 Computer Science Journal of Moldova  
In this paper we describe an ongoing work on implementation of the composition-nominative approach to program formalization in Mizar proof assistant based on the first-order logic and axiomatic set theory  ...  Other rules of the extended Floyd-Hoare logic for programs on nominative data are formalized in a similar way.  ...  logic for reasoning about properties of such programs are represented in Mizar.  ... 
doaj:a77c69ab9a394fb7854382c6ba6b81d5 fatcat:2z3et75rkneydeps4jal2jjs4i

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

James Cheney
2005 arXiv   pre-print
After an overview of other approaches, we describe nominal abstract syntax and nominal logic, a logic for reasoning about nominal abstract syntax.  ...  We also discuss applications of nominal techniques to programming, automated reasoning, and identify some future directions.  ...  Figure 4 : Closure conversion in αProlog αProlog is an example of a nominal logic programming language, that is, its logical foundation is nominal logic.  ... 
arXiv:cs/0511025v1 fatcat:sro6jwwv65f2jnmxlzsulzr7r4

An Approach To Formalization of an Extension of Floyd-Hoare Logic

Artur Kornilowicz, Andrii Kryvolap, Mykola S. Nikitchenko, Ievgen Ivanov
2017 International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications  
These data are based on the naming relation and are called nominative data. They can conveniently represent many data structures used in programming.  ...  The classical Floyd-Hoare logic is defined for the case of total pre-and postconditions and partial programs (i.e. programs can be undefined on some input data, but conditions must be defined on all data  ...  In accordance with the composition-nominative approach the semantic component of our Floyd-Hoare logic extension will be based on program algebra (a set of functions and predicates on nominative data which  ... 
dblp:conf/icteri/KornilowiczKNI17 fatcat:4by6xfgo6jfm3cy6pfcwrrwiri

The Hybrid μ-Calculus [chapter]

Ulrike Sattler, Moshe Y. Vardi
2001 Lecture Notes in Computer Science  
We present an ExpTime decision procedure for the full µ-Calculus (including converse programs) extended with nominals and a universal program, thus devising a new, highly expressive ExpTime logic.  ...  The contribution of the paper is two-fold: we extend the family of ExpTime logics, and we present a technique to reason in the presence of nominals.  ...  We are able to show that the complexity of the full µ-calculus, when extended with a universal program and nominals, does not increase, but remains in ExpTime.  ... 
doi:10.1007/3-540-45744-5_7 fatcat:5a76qrdedrfalczp3g2n5zvvpu

Extending the SMT-Lib Standard with Theory of Nominative Data

Liudmyla Omelchuk, Olena Shyshatska
2019 International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications  
Thus, in terms of composition-nominative approach, we can build systems of verification of programs based on a unified conceptual basis.  ...  By using nominative data, we can increase the level of adequacy of representation data structures, functions, and compositions that are used in programming languages.  ...  A new sublogic, or simply logic, is defined in the SMT-LIB language by a logic declaration. Logic declarations have a similar format to theory declarations.  ... 
dblp:conf/icteri/OmelchukS19 fatcat:yekqykueyre3dk6fx4mukkot3q
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