Cut-free sequent and tableau systems for propositional Diodorean modal logics:
Abstract: "We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4.3, S4.3.1 and S4.14. When the modality [square] is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear dis...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
1993
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| Series: | Computer Laboratory <Cambridge>: Technical report
288 |
| Subjects: | |
| Summary: | Abstract: "We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4.3, S4.3.1 and S4.14. When the modality [square] is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulae X the 'superformulae' involved are always bounded by a finite set of formulae X*[subscript L] depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these logics. The techniques are due to Hintikka and Rautenberg. |
| Physical Description: | 19 S. |
Staff View
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| 520 | 3 | |a Abstract: "We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4.3, S4.3.1 and S4.14. When the modality [square] is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulae X the 'superformulae' involved are always bounded by a finite set of formulae X*[subscript L] depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question | |
| 520 | 3 | |a The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these logics. The techniques are due to Hintikka and Rautenberg. | |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:04Z |
| institution | BVB |
| language | English |
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| publishDate | 1993 |
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| series | Computer Laboratory <Cambridge>: Technical report |
| series2 | Computer Laboratory <Cambridge>: Technical report |
| spelling | Goré, Rajeev Verfasser aut Cut-free sequent and tableau systems for propositional Diodorean modal logics Cambridge 1993 19 S. txt rdacontent n rdamedia nc rdacarrier Computer Laboratory <Cambridge>: Technical report 288 Abstract: "We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4.3, S4.3.1 and S4.14. When the modality [square] is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulae X the 'superformulae' involved are always bounded by a finite set of formulae X*[subscript L] depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these logics. The techniques are due to Hintikka and Rautenberg. Computer software sigle Logic programming Computer Laboratory <Cambridge>: Technical report 288 (DE-604)BV004055605 288 |
| spellingShingle | Goré, Rajeev Cut-free sequent and tableau systems for propositional Diodorean modal logics Computer Laboratory <Cambridge>: Technical report Computer software sigle Logic programming |
| title | Cut-free sequent and tableau systems for propositional Diodorean modal logics |
| title_auth | Cut-free sequent and tableau systems for propositional Diodorean modal logics |
| title_exact_search | Cut-free sequent and tableau systems for propositional Diodorean modal logics |
| title_full | Cut-free sequent and tableau systems for propositional Diodorean modal logics |
| title_fullStr | Cut-free sequent and tableau systems for propositional Diodorean modal logics |
| title_full_unstemmed | Cut-free sequent and tableau systems for propositional Diodorean modal logics |
| title_short | Cut-free sequent and tableau systems for propositional Diodorean modal logics |
| title_sort | cut free sequent and tableau systems for propositional diodorean modal logics |
| topic | Computer software sigle Logic programming |
| topic_facet | Computer software Logic programming |
| volume_link | (DE-604)BV004055605 |
| work_keys_str_mv | AT gorerajeev cutfreesequentandtableausystemsforpropositionaldiodoreanmodallogics |