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A method to single out maximal propositional logics with the disjunction property II

Mauro Ferrari, Pierangelo Miglioli
1995 Annals of Pure and Applied Logic  
iff CI GH p and p EH cc; finally, for any Kripke model K and any wff H, K/ GH will denote the quotient model of K with respect to EH defined in Section 1.4.  ...  arise) will be the set of final states of P following a; Y(9) and Y&P') will be, respectively, the (standard) logic and the regular (nonstandard) logic generated by a class 9 of frames; if L is a standard  ...  first part has appeared in this journal with the title "A method to single out maximal propositional logics with the disjunction property I".  ... 
doi:10.1016/0168-0072(94)00052-5 fatcat:y7abvafv5bbq7kp4xehmpcvmtm

Page 1427 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
Summary of Part II: “This is the second part of a paper devoted to the study of the maximal intermediate propositional logics with the disjunction property (simply called maximal constructive log- ics)  ...  Logic 76 (1995), no. 1, 1-46. 97¢:03095b 03B55 Ferrari, Mauro |Ferrari, Mauro'| (I-MILAN-I; Milan); Miglioli, Pierangelo (I-MILAN-I; Milan) A method to single out maximal propositional logics with the  ... 

A method to single out maximal propositional logics with the disjunction property I

Mauro Ferrari, Pierangelo Miglioli
1995 Annals of Pure and Applied Logic  
The present part illustrates infinitely many maximal logics with the disjunction property extending the well-known logic of Scott, and aims to provide a first picture of the method, sufficient for the  ...  This is the first part of a paper concerning intermediate propositional logics with the disjunction property which cannot be properly extended into logics of the same kind, and are therefore called maximul  ...  The present part can also be seen as a self-standing paper which should allow the reader to grasp the main lines of our method to single out maximal constructive logics even disregarding the second part  ... 
doi:10.1016/0168-0072(94)00053-6 fatcat:kmo2r6357ncwpk4x6ncuxg7s2y

Propositional team logics

Fan Yang, Jouko Väänänen
2017 Annals of Pure and Applied Logic  
We define an expressively maximal propositional team logic, called full propositional team logic. This requires going beyond the logical operations of classical propositional logic.  ...  We exhibit a hierarchy of logics between the smallest, viz. classical propositional logic, and the full propositional team logic.  ...  Acknowledgements The authors would like to thank Maria Aloni, Pietro Galliani, Lauri Hella, Juha Kontinen, Vít Punčochář, Floris Roelfsen and Dag Westerståhl for useful conversations related to this paper  ... 
doi:10.1016/j.apal.2017.01.007 fatcat:pfr2loh6zvhsrlynlx44v7x5zm

Logics of Synonymy

Levin Hornischer
2020 Journal of Philosophical Logic  
We use the notion of a scenario to get a logic of synonymy (SF) which is the canonical representative of one division.  ...  And it unveils an impossibility for synonymy: if it is to preserve subject matter, then either conjunction and disjunction lose an essential property or a very weak absorption law is violated.  ...  Then every sentence ϕ has a unique standard disjunctive normal form ϕ C with the properties corresponding to the system C (e.g. maximal, maximal positive, etc.).  ... 
doi:10.1007/s10992-019-09537-5 fatcat:gturir5urzd27bwifcbis2dwli

On the strongest three-valued paraconsistent logic contained in classical logic and its dual [article]

C. A. Middelburg
2020 arXiv   pre-print
In this paper, properties concerning the logical equivalence relation of a logic are used to distinguish LP^⊃,𝖥 from the others.  ...  In this paper, properties concerning the logical equivalence relation of a logic are also used to distinguish the paracomplete analogue of LP^⊃,𝖥 from the other three-valued paracomplete propositional  ...  Moreover, it is easy to see that property (e) is a common property of all threevalued paraconsistent propositional logics with properties (a) and (b).  ... 
arXiv:1702.03414v7 fatcat:ktigbnbsvvfbbmawecso2rksja

The Ackermann approach for modal logic, correspondence theory and second-order reduction

Renate A. Schmidt
2012 Journal of Applied Logic  
sheds light on the kinds of axioms that are equivalent to first-order correspondence properties and can be used to obtain complete axiomatizations for modal logics.  ...  This paper introduces a substitutionrewrite approach based on Ackermann's Lemma to second-order quantifier elimination in modal logic.  ...  Acknowledgements The work has benefited from discussions with Andrzej Szałas for which I am grateful. I also thank the anonymous reviewer for useful comments.  ... 
doi:10.1016/j.jal.2012.01.001 fatcat:s3bkdpqthfh6fakvrnggrc7kxy

Structured Clusters: A Framework to Reason with Contradictory Interests

O. Rodrigues
2003 Journal of Logic and Computation  
The result or conclusion of a belief base can be computed into a sentence, allowing the method to be used in the reasoning of more complex structures where nodes in the structure are themselves prioritized  ...  Priorities are given in terms of a partial pre-order associated with the sentences in the base.  ...  We represent sentences of propositional logic using the disjunctive normal form (DNF).  ... 
doi:10.1093/logcom/13.1.69 fatcat:gopmjgfjhzabxhhiijxij7xlom

Compositional verification of sequential programs with procedures

Dilian Gurov, Marieke Huisman, Christoph Sprenger
2008 Information and Computation  
We present a novel maximal model construction for the fragment of the modal -calculus with boxes and greatest fixed points only, and adapt it to control-flow graphs modelling components described in a  ...  We present a method for algorithmic, compositional verification of control-flow-based safety properties of sequential programs with procedures.  ...  Note that I is not in SNF (proposition r is missing). The maximal applet with respect to a formula φ and interface I is defined as the maximal model of φ conjoined with the interface formula for I.  ... 
doi:10.1016/j.ic.2008.03.003 fatcat:i2bb4ckl5ngp3aa6ezxzhpqt4a

Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation

Nicola Leone, Pasquale Rullo, Francesco Scarcello
1997 Information and Computation  
We then generalize the well-founded W P operator to disjunctive logic programs, give a xpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function-free  ...  The other proves that stable models can be de ned equivalently by a property of their false literals, as a model is stable i the set of its false literals coincides with its greatest unfounded set.  ...  The paper bene ted greatly from the comments of the referees for Information and Computation; they suggested that the results be extended to programs with function symbols.  ... 
doi:10.1006/inco.1997.2630 fatcat:4hf2oeyy2favlozcxyoeubxxwi

Propositional logics of dependence

Fan Yang, Jouko Väänänen
2016 Annals of Pure and Applied Logic  
In this paper, we study logics of dependence on the propositional level.  ...  We prove that several interesting propositional logics of dependence, including propositional dependence logic, propositional intuitionistic dependence logic as well as propositional inquisitive logic,  ...  Acknowledgements The authors would like to thank Ivano Ciardelli, Pietro Galliani, Lauri Hella, Taneli Huuskonen, Rosalie Iemhoff, Dick de Jongh, Juha Kontinen, Tadeusz Litak, Floris Roelofsen and Dag  ... 
doi:10.1016/j.apal.2016.03.003 fatcat:kgot2s3ufjfndd4tfx7gunsdjm

Some Properties of Linear Logic Proved by Semantic Methods

ARNON AVRON
1994 Journal of Logic and Computation  
We construct several simple algebraic models of the multiplicative and multiplicative-additive fragments of linear logic and demonstrate the value of such models by proving some unexpected proof-theoretical  ...  properties of these fragments.  ...  In situations like this in logic one usually tries to apply semantical methods.  ... 
doi:10.1093/logcom/4.6.929 fatcat:rfqpo7gntncqznqqzvk3ktgx24

Identity of Proofs Based on Normalization and Generality

Kosta Došen
2003 Bulletin of Symbolic Logic  
relation based on generality, two derivations having the same generality if after generalizing maximally the rules involved in them they yield the same premises and conclusions up to a renaming of variables  ...  The generality proposal was rather neglected in logic, though related matters were much studied in pure category theory in connection with coherence problems, and there are also links to low-dimensional  ...  A plenary address at the Logic Colloquium 2002 in Miinster was based on the present paper. I am grateful to the organizers for inviting me to deliver this talk.  ... 
doi:10.2178/bsl/1067620091 fatcat:2k56fbyssveqvfdafld4w2oovm

Hypothetical reasoning in logic programs

Katsumi Inoue
1994 The Journal of Logic Programming  
We will also apply a knowledge system to the closed world assumption.  ...  Find an explanation E (L H) of a formula 0 such that 6) T U E is consistent and (ii) 0 is derived from TUE.  ...  The method is to replace every classical negation in a program II with a new propositional symbol, for example, 1A is replaced by A'.  ... 
doi:10.1016/0743-1066(94)90043-4 fatcat:epm6iwmfurgpnmwuuhecfrz4am

K3, L3, LP, RM3, A3, FDE: How to Make Many-Valued Logics Work for You [article]

Allen P. Hazen, Francis Jeffry Pelletier
2017 arXiv   pre-print
At the end, we show some surprising results in the system FDE, and its relationships with features of other logics. We close with some new examples of "synonymous logics."  ...  We investigate some well-known (and a few not-so-well-known) many-valued logics that have a small number (3 or 4) of truth values.  ...  Given A not derivable from Γ, it is readily seen that a set maximal with respect to the property of containing Γ but not implying A will be eligible in this sense, and the existence of such a maximal set  ... 
arXiv:1711.05816v1 fatcat:sc2kiksk5vaz5fdzrgfp6ncrbu
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