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Intuitionistic propositional logic with Galois connections

W. Dzik, J. Jarvinen, M. Kondo
2009 Logic Journal of the IGPL  
Duality between algebraic and Kripke semantics is presented, and a representation theorem for Heyting algebras with Galois connections is proved.  ...  In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections.  ...  Acknowledgement We would like to take the opportunity to thank the anonymous referees for their comments and suggestions which helped us to improve the paper.  ... 
doi:10.1093/jigpal/jzp057 fatcat:gm5gcpwp6famnliqg7isktvuvi

Intuitionistic logic with two Galois connections combined with Fischer Servi axioms [article]

Wojciech Dzik, Jouni Järvinen, Michiro Kondo
2012 arXiv   pre-print
Both Kripke-style and algebraic semantics are presented for Int2GC and Int2GC+FS, and the logics are proved to be complete with respect to both of these semantics.  ...  Earlier, the authors introduced the logic IntGC, which is an extension of intuitionistic propositional logic by two rules of inference mimicking the performance of Galois connections (Logic J. of the IGPL  ...  Introduction and Motivation In [15] , Information Logic of Galois Connections (ILGC) was introduced as classical propositional logic with a pair of unary connectives and ▽ mimicking a Galois connection  ... 
arXiv:1208.2971v1 fatcat:lact2xfl4vb5jheyi3juj6nom4

Characterizing intermediate tense logics in terms of Galois connections

W. Dzik, J. Jarvinen, M. Kondo
2014 Logic Journal of the IGPL  
This is done by building the fusion of two copies of intermediate logic with a Galois connection LGC, and then interlinking their operators by two Fischer Servi axioms.  ...  Orlowska and I. Rewitzky. For each intermediate logic L, we show algebraic completeness of L2GC+FS and its conservativeness over L.  ...  It is well know that many intermediate logics are Kripke-incomplete, or their Kripke-completeness is not known.  ... 
doi:10.1093/jigpal/jzu024 fatcat:bnalmdg6ebbaleb3lmowc7mpay

Bi-approximation Semantics for Substructural Logic at Work

Tomoyuki Suzuki
2010 Advances in Modal Logic  
Moreover, by introducing the bi-directional approximation and bases, we track down a connection to Kripke-type semantics for distributive substructural logics through a relationship between basis and the  ...  along a back-and-force correspondences.  ...  Unlike Kripke semantics for modal logic, we can find several types of relational semantics for substructural logic based on their philosophy or on their mathematical frameworks.  ... 
dblp:conf/aiml/Suzuki10 fatcat:d3yg24ftafewjmq3ka3tnlxiva

Page 2188 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
logic LJ and that all formulae which are derivable in LJ are true in all Kripke frames (and thus in all Kripke frames with finite domains).  ...  In the paper the author considers the fragment of intuitionis- tic predicate logic without disjunction and existential quantifier, LJ'*”~-+}_ He constructs a Kripke frame with finite domain TL such that  ... 

Generalized Kripke semantics for the Lambek-Grishin calculus

A. Chernilovskaya, M. Gehrke, L. van Rooijen
2012 Logic Journal of the IGPL  
Here, we consider semantics based on the generalised Kripke frames naturally associated with the algebraic semantics of the logics in question via their representation theory.  ...  However, in Kripke-style semantics for intuitionistic logic, frames are equipped with an order and interpretants must be hereditary sets.  ... 
doi:10.1093/jigpal/jzr051 fatcat:6xcparlsorf3lgam2it6s4lory

Rough concepts [article]

Willem Conradie, Sabine Frittella, Krishna Manoorkar, Sajad Nazari, Alessandra Palmigiano, Apostolos Tzimoulis, Nachoem M. Wijnberg
2020 arXiv   pre-print
Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original approximation spaces can be seen as special instances of enriched  ...  The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis.  ...  Enriched formal contexts and their complex algebras In [15] , structures similar to the following are introduced as generalizations of Kripke frames. Definition 2.5.  ... 
arXiv:1907.00359v2 fatcat:ve7ptw7brvcdro524532qa3lnu

Logics from Galois connections

Jouni Järvinen, Michiro Kondo, Jari Kortelainen
2008 International Journal of Approximate Reasoning  
Namely, a certain composition of Galois connection mappings forms a lattice-theoretical interior operator, and this motivates us to axiomatize a logic of these compositions.  ...  In addition to the three classical propositional logic axioms and the inference rule of modus ponens, ILGC contains only two auxiliary rules of inference mimicking the performance of Galois connections  ...  Acknowledgements The authors thank the anonymous referees for their comments and several improvements. Jouni Järvinen wants also to thank Wojciech Dzik for fruitful discussions.  ... 
doi:10.1016/j.ijar.2008.06.003 fatcat:rk4lvk6yvna2xpqiqqbixfwuoq

An algebraic view of space/belief and extrusion/utterance for concurrency/epistemic logic

Stefan Haar, Salim Perchy, Camilo Rueda, Frank Valencia
2015 Proceedings of the 17th International Symposium on Principles and Practice of Declarative Programming - PPDP '15  
We shall investigate the properties of this new family of constraint systems and illustrate their applications.  ...  We enrich spatial constraint systems with operators to specify information and processes moving from a space to another.  ...  Acknowledgements We would like to thank Moreno Falaschi, Thomas Given-Wilson, Michell Guzman, Sophia Knight and Carlos Olarte for their insights and discussions on some preliminary ideas of this work.  ... 
doi:10.1145/2790449.2790520 dblp:conf/ppdp/HaarPRV15 fatcat:7zxo5olw4vhvppjc5x4cc35m7y

Relational semantics for full linear logic

Dion Coumans, Mai Gehrke, Lorijn van Rooijen
2014 Journal of Applied Logic  
Relational semantics, given by Kripke frames, play an essential role in the study of modal and intuitionistic logic.  ...  Building on these ideas, in [Geh06] a type of frames is described which generalise Kripke frames and provide semantics for substructural logics in a purely relational form.  ...  A class of frames (RS-frames) is described which generalise Kripke frames and provide semantics for substructural logics in a purely relational form.  ... 
doi:10.1016/j.jal.2013.07.005 fatcat:maboqq7sgjbjdd2rhfv2jxslu4

Belief, knowledge, lies and other utterances in an algebra for space and extrusion

Michell Guzman, Stefan Haar, Salim Perchy, Camilo Rueda, Frank D. Valencia
2017 Journal of Logical and Algebraic Methods in Programming  
Constraint systems are often represented as lattices: their elements, called constraints, represent partial information and their order corresponds to entailment.  ...  We shall investigate the properties of this new family of constraint systems and illustrate their applications.  ...  We thank Moreno Falaschi, Sophia Knight, Carlos Olarte, and Hans van Ditmarsch for their feedback on earlier versions of this work.  ... 
doi:10.1016/j.jlamp.2016.09.001 fatcat:jtnvslgy2ve5bbizgfgqjs4fci

Categories: How I Learned to Stop Worrying and Love Two Sorts [article]

Willem Conradie, Sabine Frittella, Michele Piazzai, Apostolos Tzimoulis, Alessandra Palmigiano, Nachoem M. Wijnberg
2016 arXiv   pre-print
We propose an intuitive, epistemic interpretation of RS-frames for modal logic, in terms of categorization systems and agents' subjective interpretations of these systems.  ...  RS-frames were introduced by Gehrke as relational semantics for substructural logics. They are two-sorted structures, based on RS-polarities with additional relations used to interpret modalities.  ...  Preliminaries In this section we recall some preliminaries on perfect lattices, RS-polarities, generalized Kripke frames and formal concept analysis.  ... 
arXiv:1604.00777v2 fatcat:3mspaxajcnfjhexrvxf3fchuvy

Categories: How I Learned to Stop Worrying and Love Two Sorts [chapter]

Willem Conradie, Sabine Frittella, Alessandra Palmigiano, Michele Piazzai, Apostolos Tzimoulis, Nachoem M. Wijnberg
2016 Lecture Notes in Computer Science  
We propose an intuitive, epistemic interpretation of RS-frames for modal logic, in terms of categorization systems and agents' subjective interpretations of these systems.  ...  RS-frames were introduced by Gehrke as relational semantics for substructural logics. They are two-sorted structures, based on RS-polarities with additional relations used to interpret modalities.  ...  Preliminaries In this section we recall some preliminaries on perfect lattices, RS-polarities, generalized Kripke frames and formal concept analysis.  ... 
doi:10.1007/978-3-662-52921-8_10 fatcat:uyucniebjjd27dxhrsvagvqtya

Autoreferential semantics for many-valued modal logics

Zoran Majkic
2008 Journal of Applied Non-Classical Logics  
We define the autoreferential set-based representation for the class of modal algebras, and show that the autoreferential Kripke-style semantics for this class of modal algebras is based on the set of  ...  can be accepted by this world, then we connect it with paraconsistent properties and LFI logics.  ...  Acknowledgements The author wish to thank Walter Carnielli for his support and useful comments about earlier version of this paper, about paraconsistency and LFI.  ... 
doi:10.3166/jancl.18.79-125 fatcat:moeq23z5rnba3pzxa5ndqjuv5a

Weakening of Intuitionistic Negation for Many-valued Paraconsistent da Costa System

Zoran Majkić
2008 Notre Dame Journal of Formal Logic  
After that we define Kripke style semantics based on possible worlds, and derive from it manyvalued semantics based on truth-functional valuations, for these two paraconsistent logics.  ...  Finally we demonstrate that this model-theoretic inference system is adequate: sound and complete w.r.t. the axiomatic da Costa like systems for these two logics.  ...  subformulae in other possible worlds mediated by the defined binary accessibility relation of a Kripke frame.  ... 
doi:10.1215/00294527-2008-020 fatcat:vpr2jxlgb5bulncfxbuwmw5k3a
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