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From inconsistency handling to non-canonical requirements management: A logical perspective

Kedian Mu, Jun Hong, Zhi Jin, Weiru Liu
2013 International Journal of Approximate Reasoning  
We first argue that measuring non-canonical requirements plays a crucial role in handling them effectively. We then present a measure-driven logic framework for managing non-canonical requirements.  ...  This generalization can be considered as an attempt to handle non-canonical requirements along with logic-based inconsistency handling in requirements engineering.  ...  For example, Hunter and Nuseibeh [2] developed labeled quasi-classic logic to represent and reason about requirements specifications in the presence of inconsistency.  ... 
doi:10.1016/j.ijar.2012.07.006 fatcat:fsgdylowgvbpfd5kkrnenxjgxu

Modality and Contextuality in Topos Quantum Theory

Benjamin Eva
2016 Studia Logica: An International Journal for Symbolic Logic  
In this paper, we investigate the relationship between these two logical structures and study the implications of this relationship for the definition of modal operators in TQT.  ...  Topos quantum theory (TQT) represents a whole new approach to the formalization of non-relativistic quantum theory.  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s11225-016-9668-x fatcat:dquhux3hifee5fivobujyiqpwa

Sahlqvist via Translation [article]

Willem Conradie, Alessandra Palmigiano, Zhiguang Zhao
2018 arXiv   pre-print
This definition covers in particular all (bi-)intuitionistic modal logics.  ...  The theory of these logics has been intensively studied over the past seventy years in connection with classical polyadic modal logics, using suitable versions of Goedel-McKinsey-Tarski translations as  ...  ) modal logic to logics of arbitrary normal distributive lattice expansions and, in a more restricted setting, the transfer of generalized Sahlqvist canonicity from multi-modal (classical) modal logic  ... 
arXiv:1603.08220v3 fatcat:5hayhcbahfao7b6rt2vdkgpahy

Algorithmic correspondence for relevance logics, bunched implication logics, and relation algebras: the algorithm PEARL and its implementation (Technical Report) [article]

Willem Conradie, Valntin Goranko, Peter Jipsen
2021 arXiv   pre-print
This generalizes the "canonicity via correspondence" result in Urquhart's 1996 paper.  ...  of formulas of the language of relevance logics RL in terms of the standard Routley-Meyer relational semantics.  ...  Introduction This work relates two important areas of development in non-classical logics, viz. relevance logics and algorithmic correspondence theory, by applying the latter to the possible worlds semantics  ... 
arXiv:2108.06603v1 fatcat:xn3ha3ic7raereezm2stcy5nqu

Page 1690 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
) Bridges between classical and nonmonotonic logic.  ...  These geometries include the bi- linear one mentioned above (also in projective and affine guises), 03 MATHEMATICAL LOGIC AND FOUNDATIONS 1690 and also a certain ‘quadratic geometry’; this is the collection  ... 

On the logical structure of choice and bar induction principles

Nuria Brede, Hugo Herbelin
2021 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
up to weak classical reasoning GBIABT intuitionistically captures • the strength of Gödel's completeness theorem in the form validity implies provability for entailment relations when B = B, • the strength  ...  After classifying and analysing the relations between different intensional definitions of ill-foundedness and well-foundedness, we introduce, for a domain A, a codomain B and a "filter" T on finite approximations  ...  Acknowledgments We thank the communities of researchers who contributed to develop the material we built on, and in particular Camille Noûs, from the Cogitamus Lab, who embodies the collective and collaborative  ... 
doi:10.1109/lics52264.2021.9470523 fatcat:bfwohvtglfb6jlijnuns653w3u

Canonicity results for mu-calculi: an algorithmic approach

Willem Conradie, Andrew Craig
2017 Journal of Logic and Computation  
This latter concept has previously been investigated for the classical mu-calculus by Bezhanishvili and Hodkinson. Our approach is in the spirit of Sahlqvist theory.  ...  In the algebraic setting of canonical extensions we examine both the usual notion of canonicity and what we will call tame canonicity.  ...  In this paper we will make use of purely algebraic and order-theoretic techniques. This approach has proved fruitful in obtaining completeness results for many non-classical logics.  ... 
doi:10.1093/logcom/exx011 fatcat:zj66pbutu5gb3byt3bgg3nlyyi

Canonicity results for mu-calculi: an algorithmic approach [article]

Willem Conradie, Andrew Craig
2014 arXiv   pre-print
This latter concept has previously been investigated for the classical mu-calculus by Bezhanishvili and Hodkinson. Our approach is in the spirit of Sahlqvist theory.  ...  In the algebraic setting of canonical extensions we examine both the usual notion of canonicity and what we will call tame canonicity.  ...  In this paper we will make use of purely algebraic and order-theoretic techniques. This approach has proved fruitful in obtaining completeness results for many non-classical logics.  ... 
arXiv:1408.6367v1 fatcat:ik4kcvgvgffknfuancwyram3au

Expressivity Properties of Boolean BI Through Relational Models [chapter]

Didier Galmiche, Dominique Larchey-Wendling
2006 Lecture Notes in Computer Science  
Loosely dened by Pym as BI + {¬¬A → A} -no known pure sequent based proof system -Kripke semantics is non-deterministic (Larchey&Galmiche) -faithfully embeds S4 and thus IL Other denition (logical core  ...  of Separation and Spatial logics) -additive implication → Kripke interpreted classically based on (commutative) partial monoids (M; •) -has a sound and complete (labelled tableaux) proof-system still  ... 
doi:10.1007/11944836_33 fatcat:bfma3l6cajd7vgcuxyqmuffydi

Constructive Canonicity of Inductive Inequalities

Willem Conradie, Alessandra Palmigiano
2018 Logical Methods in Computer Science  
We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice expansions.  ...  This result encompasses Ghilardi-Meloni's and Suzuki's constructive canonicity results for Sahlqvist formulas and inequalities, and is based on an application of the tools of unified correspondence theory  ...  In [37] , duality, correspondence and canonicity are developed for classical modal logic on possibility frames, where filter-canonicity is understood as the preservation of the validity of formulas from  ... 
doi:10.23638/lmcs-16(3:8)2020 fatcat:urs56m5kxzfrxk4gmj2zjfxmze

Constructive Canonicity of Inductive Inequalities [article]

Willem Conradie, Alessandra Palmigiano
2020 arXiv   pre-print
We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice expansions.  ...  This result encompasses Ghilardi-Meloni's and Suzuki's constructive canonicity results for Sahlqvist formulas and inequalities, and is based on an application of the tools of unified correspondence theory  ...  In [37] , duality, correspondence and canonicity are developed for classical modal logic on possibility frames, where filter-canonicity is understood as the preservation of the validity of formulas from  ... 
arXiv:1603.08341v4 fatcat:hq3t3x277jf2fphwryt4kslv7i

The Vertical Logic of Hamiltonian Methods (Part 1) [article]

C. Baumgarten
2022 arXiv   pre-print
We demonstrate that a derivation of these core concepts of modern physics requires little more than a proper formulation in terms of classical Hamiltonian theory.  ...  We discuss the key role that Hamiltonian notions play in physics. Five examples are given that illustrate the versatility and generality of Hamiltonian notions.  ...  Röcken for comments and critical remarks. L A T E X has been used to write this article, XFig 3.2.5 for the figures. Mathematica ® has originally been used for parts of the symbolic calculations.  ... 
arXiv:2001.03412v6 fatcat:hmuvyja2aza7tiwzauerwquh5a

On the logical structure of choice and bar induction principles [article]

Nuria Brede, Hugo Herbelin
2022 arXiv   pre-print
B = 𝔹 (up to weak classical reasoning): GBI_A,B,T intuitionistically captures the strength of∙ Gödel's completeness theorem in the form validity implies provability for entailment relations if B = 𝔹  ...  After classifying and analysing the relations between different intensional definitions of ill-foundedness and well-foundedness, we introduce, for a domain A, a codomain B and a "filter" T on finite approximations  ...  ACKNOWLEDGMENTS We thank the communities of researchers who contributed to develop the material we built on, and in particular Camille Noûs, from the Cogitamus Lab, who embodies the collective and collaborative  ... 
arXiv:2105.08951v3 fatcat:xriu572dqjeqrobtr546e7j23a

On linguistic approximation of uncertainty quantities based on signal-noise ratio

M. Ahmadi Anvigh
2013 Communications on Advanced Computational Science with Applications  
Our own approach to defuzzification, which is described in the paper in more details, is based on relevant measures of uncertainty-based information.  ...  Another application of this defuzzification noticed in end of article.  ...  The crux of this program is to approximate perceptions by statements in natural language and, then, to use fuzzy logic to represent these statements and deal with them as needed.  ... 
doi:10.5899/2013/cacsa-00008 fatcat:2yyzb3d2wrbgvc2ftyh65oizda

Quantum simplicial dynamics

David Finkelstein
2011 Journal of Physics, Conference Series  
This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups.  ...  Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity.  ...  Quantum theory replaced Boolean logic by a projective logic. This destroyed classical quantification theory at its Boolean base and necessitated a quantum replacement.  ... 
doi:10.1088/1742-6596/330/1/012001 fatcat:t7zqtmxad5ejtbik35ho54uobe
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