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Description of modal logics inheriting admissible rules for S4
1999
Logic Journal of the IGPL
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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
2008
Logic Journal of the IGPL
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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
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(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
2009
Journal of Symbolic Logic (JSL)
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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
2013
Acta Informatica
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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
2005
Journal of Logic and Computation
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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
2009
Theory of Computing Systems
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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]
1996
Lecture Notes in Computer Science
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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]
1999
Lecture Notes in Computer Science
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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
2014
Logica Universalis
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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
2000
Information and Computation
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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]
2017
arXiv
pre-print
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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
2000
Information and Computation
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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
1990
Annals of Pure and Applied Logic
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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
2015
Annals of Pure and Applied Logic
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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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