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From inconsistency handling to non-canonical requirements management: A logical perspective
2013
International Journal of Approximate Reasoning
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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
2016
Studia Logica: An International Journal for Symbolic Logic
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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]
2018
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
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)
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
2021
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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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
2017
Journal of Logic and Computation
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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]
2014
arXiv
pre-print
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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]
2006
Lecture Notes in Computer Science
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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
2018
Logical Methods in Computer Science
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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]
2020
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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
2013
Communications on Advanced Computational Science with Applications
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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
2011
Journal of Physics, Conference Series
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2011 pre-print arXiv:1108.1495v1 fatcat:4u2kbvucsvhrrb5dozeg65yrpy
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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