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Description of modal logics inheriting admissible rules for S4

V. Rybakov
1999 Logic Journal of the IGPL  
Using this condition we describe all tabular modal logics inheriting inference rules admissible for S4.  ...  We give a necessary and sufficient condition for any modal logic with fmp to inherit all inference rules admissible in S4.  ...  Dept. of Science Faculty of Ege University, Bornova-Izmir, Turkey in 1997/1998.  ... 
doi:10.1093/jigpal/7.5.655 fatcat:4fahyok2hraydfyhm653mms2qq

Independent Bases of Admissible Rules

E. Jerabek
2008 Logic Journal of the IGPL  
We show that IPC , K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules.  ...  Similar bases for admissible rules of some modal logics were constructed by Jeřábek [10] . A basis for admissible rules of S4 was also constructed earlier by Rybakov [14] .  ...  A simple description of all logics inheriting multiple-conclusion admissible rules of K4 or S4 was given in [11] ; in particular, the largest such logics are K4Grz and S4Grz , respectively. basis logic  ... 
doi:10.1093/jigpal/jzn004 fatcat:5uwvxesrcbdi7okaqm5zzjvv6m

Page 6796 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
(TR-EGES; Izmir) Description of modal logics inheriting admissible rules for S4. (English summary) Log. J. IGPL 7 (1999), no. 5, 655-664.  ...  This characterization is used to describe the tabular logics inheriting all rules admissible for S4. J. M. Plotkin (1-MIS; East Lansing, MI) 2000j:03036 03B45 68Q60 van der Torre, Leendert W. N.  ... 

Canonical rules

Emil Jeřábek
2009 Journal of Symbolic Logic (JSL)  
We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible  ...  Other applications of canonical rules include a generalization of the Blok–Esakia theorem and the theory of modal companions to systems of multiple-conclusion rules or (unitary structural global) consequence  ...  property, and a recursive basis of admissible multiple-conclusion rules consisting of the basis for L 0 from Theorem 4.11 If a logic L inherits single-conclusion admissible rules of IPC , K4, GL, S4  ... 
doi:10.2178/jsl/1254748686 fatcat:4mt72ynkybhihaaonpwt5w64xe

Judgmental subtyping systems with intersection types and modal types

Jeongbong Seo, Sungwoo Park
2013 Acta Informatica  
We study how to extend modal type systems based on intuitionistic modal logic S4 or S5 with a subtyping system based on intersection types.  ...  We use the proof assistant Coq to prove the admissibility of the cut rules and the equivalence between the two kinds of subtyping systems.  ...  In our study of a subtyping system based on modal logic S4, for example, we discover the need for the following subtyping rule only during the proof of its equivalence with another subtyping system: C  ... 
doi:10.1007/s00236-013-0186-2 fatcat:rkmimqrsznfcxdizdw25eyjtuy

Admissible Rules of Modal Logics

Emil Jeřábek
2005 Journal of Logic and Computation  
We construct explicit bases of admissible rules for a representative class of normal modal logics (including the systems K4, GL, S4, Grz, and GL.3), by extending the methods of S. Ghilardi and R.  ...  We also investigate the notion of admissible multiple conclusion rules.  ...  question), and settled various properties of sets of admissible rules and their bases (e.g., non-existence of finite bases of admissible rules for IP C and certain modal logics).  ... 
doi:10.1093/logcom/exi029 fatcat:tksfg63qvrchvaplums5ea4fb4

Self-Referential Justifications in Epistemic Logic

Roman Kuznets
2009 Theory of Computing Systems  
We consider well-known modal logics of knowledge/belief and show, using explicit justifications, that S4, D4, K4, and T with their respective justification counterparts LP, JD4, J4, and JT describe knowledge  ...  The goal is to investigate whether such self-referential justifications are present in the reasoning described by standard modal epistemic logics such as S4.  ...  The author thanks the anonymous referees for careful reading and useful suggestions.  ... 
doi:10.1007/s00224-009-9209-3 fatcat:eqdmoghva5dfrkq3xesjrb5zkq

A uniform proof procedure for classical and non-classical logics [chapter]

Jens Otten, Christoph Kreitz
1996 Lecture Notes in Computer Science  
It can be applied to intuitionistic and modal logics by modifying the component for testing complementarity of connected atoms.  ...  We present a proof procedure for classical and non-classical logics.  ...  Let L be one of the modal logics D, D4, S4, S5 or T.  ... 
doi:10.1007/3-540-61708-6_70 fatcat:5tvjssygyrgwtmthlk73gjbuyy

Logic-Based Knowledge Representation [chapter]

Franz Baader
1999 Lecture Notes in Computer Science  
After a short analysis of the requirements that a knowledge representation language must satisfy, we introduce Description Logics, Modal Logics, and Nonmonotonic Logics as formalisms for representing,  ...  At the end of each section, we brie y comment on the connection to Logic Programming.  ...  Figure 3 Figure 3 : 33 axiom schemata and inference rules for modal logics.  ... 
doi:10.1007/3-540-48317-9_2 fatcat:udsbpeh5anenzcktptdb4g7w34

Proofs and Countermodels in Non-Classical Logics

Sara Negri
2014 Logica Universalis  
Finitizations for intuitionistic propositional logic are obtained through the search for a minimal derivation, through pruning of infinite branches in search trees by means of a suitable syntactic counterpart  ...  The limitation is encountered also for decidable non-classical logics in traditional completeness proofs based on Henkin's method of maximal consistent sets of formulas.  ...  Such decision procedures work not just for simple logics like intuitionistic logic or S4, but also for logics such intuitionistic multi-modal logics [Garg, Genovese and Negri, 2012] , linear temporal  ... 
doi:10.1007/s11787-014-0097-1 fatcat:yzxgrtllgrga5j3nsc4qm5hgoy

Structuring Metatheory on Inductive Definitions

David Basin, Seán Matthews
2000 Information and Computation  
We use the example of the deduction theorem for modal logic and show how a statement about a theory can explicitly formalize the closure conditions extensions should satisfy for it to remain true.  ...  There are true statements about a theory that are true of some (but only some) extensions; however, standard theory-structuring facilities do not support selective inheritance.  ...  Although it is not immediate, our metatheorem provides a basis for giving a natural deduction presentation of modal logics like S4 that is essentially equivalent to Prawitz; see [1, Section 4.4] for  ... 
doi:10.1006/inco.2000.2858 fatcat:am3mm6zv2vegjf4syvnx2c7ifu

Modularisation of Sequent Calculi for Normal and Non-normal Modalities [article]

Björn Lellmann, Elaine Pimentel
2017 arXiv   pre-print
dependent multimodal logics, and for many standard non-normal modal logics.  ...  By proposing local versions to ordinary sequent rules we obtain linear nested sequent calculi for a number of logics, including to our knowledge the first nested sequent calculi for a large class of simply  ...  We thank the anonymous reviewers for their valuable comments on an earlier draft of this paper.  ... 
arXiv:1702.08193v2 fatcat:axenvawjrfhtzmphlp5clbhdcq

A Uniform Procedure for Converting Matrix Proofs into Sequent-Style Systems

Christoph Kreitz, Stephan Schmitt
2000 Information and Computation  
We present a uniform algorithm for transforming machine-found matrix proofs in classical, constructive, and modal logics into sequent proofs.  ...  It is based on unified representations of matrix characterizations, of sequent calculi, and of prefixed sequent systems for various logics.  ...  (ii) When a $-rule is applied, then C B :=C B _ [a]. (iii) When a modal rule is applied, i.e., a ?-rule for all modal logics or a ?Â&-rule for D, D4, again C B :=[c$] for a new c$.  ... 
doi:10.1006/inco.2000.2913 fatcat:a6mbazpvaffmfbqzcc7rze7jf4

Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus

V.V. Rybakov
1990 Annals of Pure and Applied Logic  
Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework.  ...  As corollaries we obtain: (a) there exists an algorithm for the recognition of admissibility of rules with parameters (hence also without them) in the modal system Grz, (b) the substitution problem for  ...  The connection between admissible rules in extensions of H and admissible rules of modal logics was observed in [17] . This connection draws attention to admissible rules of modal logics.  ... 
doi:10.1016/0168-0072(90)90055-7 fatcat:xbpyd36q6ndghgx6w44j4fzdnm

Rules with parameters in modal logic I

Emil Jeřábek
2015 Annals of Pure and Applied Logic  
We construct explicit bases of admissible rules with parameters for cluster-extensible logics, and give their semantic description.  ...  We study admissibility of inference rules and unification with parameters in transitive modal logics (extensions of K4), in particular we generalize various results on parameter-free admissibility and  ...  Admissible rules of basic transitive modal logics (K4, S4, GL, Grz, S4.3, . . . ) are fairly well understood.  ... 
doi:10.1016/j.apal.2015.04.004 fatcat:rfihurobc5genaqt7fllbwt5bu
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