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|`$modal`|`$domains`| Selects whether quantification semantics is varying domains, constant domains, cumulative domains or decreasing domains.<br><br>Accepted values: `$varying`, `$constant`, `$cumulative`, `$decreasing`|
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||`$designation`| Selects whether non-logical symbols (constants and function symbols) have rigid or flexible designation (i.e., the same interpretation in all worlds, or possibly different ones in different worlds).<br><br> Accepted values: `$rigid`, `$flexible`|
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||`$terms`| Selects whether terms, in each world `w`, are interpreted as elements from the respective domain at `w` (i.e., whether they exist in that world); this case is referred to as local terms. With global terms, terms may be interpreted as elements from arbitrary worlds (i.e., in particular, the interpretation of a term at a specific world may not exist exist at that world). <br><br> Accepted values: `$local`, `$global`|
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||`$modalities`| Selects the properties for the modal operators.<br><br> Accepted values, for each modality: `$modal_system_X` where `X` ∈ {`K`, `KB`, `K4`, `K5`, `K45`, `KB5`, `D`, `DB`, `D4`, `D5`, `D45`, `T`, `B`, `S4`, `S5`, `S5U`} <br>_or a list of axiom schemes_<br> [`$modal axiom X1` , ..., `$modal axiom Xn`]`Xi` ∈ {`K`, `T`, `B`, `D`, `4`, `5`, `CD`, `C4`} |
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|`$$hybrid`|_same as `$modal`_||
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|`$$hybrid`|_same as `$modal`_ (except that `$terms` is not available, yet). ||
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|`$$pal`|_none_||
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|`$$ddl`|`$$system`| Selects which DDL logic system is employed: Carmo and Jones or Åqvist's system E.<br><br>Accepted values: `$$carmoJones` or `$$aqvistE`|
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|`$$normative`|`$logic`| Selects which deontic logic system should be used for compiling the semantically underspecified statements into concrete expressions. <br><br> Accepted values: `$$sdl` for SDL, `$$carmoJones` for the DDL of Carmo and Jones, `$$aqvistE` for Aqvist's DDL E ||
@@ -52,6 +54,7 @@ modal logic model is non-cumulative.
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tff(modal_k5, logic, $modal == [
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$designation == $rigid,
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$domains == $decreasing,
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$terms == $local,
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$modalities == [$modal_axiom_K, $modal_axiom_5]
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] ).
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@@ -108,6 +111,7 @@ thf(advanced,logic,(
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$modal ==
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[ $designation == $rigid,
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$domains == $cumulative,
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$terms == $global,
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$modalities ==
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[ $modal_system_S5,
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{$box(#a)} == $modal_system_KB,
@@ -125,6 +129,7 @@ thf(quantification,logic,(
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$domains ==
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[ $constant,
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human_type == $varying ],
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$terms == $global,
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$modalities == $modal_system_S5 ] )).
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```
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Here, every quantification over variables of type `human_type` are varying domain, all others constant domain.
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