Temat: Modal logic S5 - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1
Autorzy:: Pietruszczak, Andrzej
Powiązania:: https://bibliotekanauki.pl/articles/749944.pdf
Data publikacji:: 2017
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: first-degree theses of modal logics
theses without iterated modalities
Pollack’s theory of Basic Modal Logic
basic theories for modal logics between C1 and S5
Opis:: This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities (i.e., the same first-degree theses).
Źródło:: Bulletin of the Section of Logic; 2017, 46, 1/2
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On Theses without Iterated Modalities of Modal Logics Between C1 and S5. Part 2
Autorzy:: Pietruszczak, Andrzej
Powiązania:: https://bibliotekanauki.pl/articles/750008.pdf
Data publikacji:: 2017
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: first-degree theses of modal logics
theses without iterated modalities
Pollack’s theory of Basic Modal Logic
basic theories for modal logics between C1 and S5
Opis:: This is the second, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only on which of the following formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨☐q⌝, and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and (T) and (altn) have no common atom. We generalize Pollack’s result from [1], where he proved that all modal logics between S1 and S5 have the same theses which does not involve iterated modalities (i.e., the same first-degree theses).
Źródło:: Bulletin of the Section of Logic; 2017, 46, 3/4
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus
Autorzy:: Indrzejczak, Andrzej
Powiązania:: https://bibliotekanauki.pl/articles/749928.pdf
Data publikacji:: 2016
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: Modal logic S5
decidability
normal forms
sequent calculus
Opis:: In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi (SC) for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form.
Źródło:: Bulletin of the Section of Logic; 2016, 45, 2
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Unifiability and Structural Completeness in Relation Algebras and in Products of Modal Logic S5
Autorzy:: Dzik, Wojciech
Wróbel, Beniamin
Powiązania:: https://bibliotekanauki.pl/articles/749956.pdf
Data publikacji:: 2015
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: admissible rules
passive rules
unification
projective unification
almost structural completeness
n-modal logic S5n
relation algebras
representable diagonal-free cylindric algebras
Opis:: Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5n a basis for admissible rules and the form of all passive rules are provided.
Źródło:: Bulletin of the Section of Logic; 2015, 44, 1-2
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

Artykuł

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