WiSe22/23: Constraint-based Semantics 2 - Revision history

Manfred: /* Basic assumptions */

2022-11-11T18:57:43Z

Basic assumptions

← Older revision		Revision as of 18:57, 11 November 2022
Line 66:		Line 66:
	We assume:		We assume:
	* Our model contains a set of possible worlds ''W'', and a set of accessiblity relations ''ACC'', i.e. M = < ''U'', ''I'', ''W'', ''ACC'' >		* Our model contains a set of possible worlds ''W'', and a set of accessiblity relations ''ACC'', i.e. M = < ''U'', ''I'', ''W'', ''ACC'' >
	* There is a special variable, ''w''<sub>0</sub> or ''ω'', or ''@'' that refers to the current world: [[''w''<sub>0</sub>]]<sup>M,w</sup> = w		* There is a special variable, ''w''<sub>0</sub> (abbreviated as ''ω'' or ''@'') that refers to the current world: [[''w''<sub>0</sub>]]<sup>M,w</sup> = w
	* There are special predicates for the different accessibility relations (modal bases):		* There are special predicates for the different accessibility relations (modal bases):
	** Alethic: '''ALETH'''<sub>sst</sub>		** Alethic: '''ALETH'''<sub>sst</sub>

Manfred: /* Basic assumptions */

2022-11-11T18:56:27Z

Basic assumptions

← Older revision		Revision as of 18:56, 11 November 2022
Line 66:		Line 66:
	We assume:		We assume:
	* Our model contains a set of possible worlds ''W'', and a set of accessiblity relations ''ACC'', i.e. M = < ''U'', ''I'', ''W'', ''ACC'' >		* Our model contains a set of possible worlds ''W'', and a set of accessiblity relations ''ACC'', i.e. M = < ''U'', ''I'', ''W'', ''ACC'' >
	* There is a special variable, ''w''<sub>0</sub> or ''ω'' that refers to the current world: [[''w''<sub>0</sub>]]<sup>M,w</sup> = w		* There is a special variable, ''w''<sub>0</sub> or ''ω'', or ''@'' that refers to the current world: [[''w''<sub>0</sub>]]<sup>M,w</sup> = w
	* There are special predicates for the different accessibility relations (modal bases):		* There are special predicates for the different accessibility relations (modal bases):
	** Alethic: '''ALETH'''<sub>sst</sub>		** Alethic: '''ALETH'''<sub>sst</sub>

Manfred: /* Example formulae */

2022-11-11T18:55:52Z

Example formulae

← Older revision		Revision as of 18:55, 11 November 2022
Line 95:		Line 95:
	''A linguist necessarily likes logic.'' (deontic necessity, without cognitive agent)		''A linguist necessarily likes logic.'' (deontic necessity, without cognitive agent)
	* &Square; ∃''x''('''linguist'''(''x'') : '''like-logic'''(''x''))		* &Square; ∃''x''('''linguist'''(''x'') : '''like-logic'''(''x''))
	:: &equiv; ∃''w'' (''w''=''ω'': ∀''@''('''DEON1'''(''w'',''ω''): ∃''x''('''linguist'''(''ω'',x) : '''like-logic'''(''ω'',''x''))))		:: &equiv; ∃''w'' (''w''=''ω'': ∀''ω''('''DEON1'''(''w'',''ω''): ∃''x''('''linguist'''(''ω'',x) : '''like-logic'''(''ω'',''x''))))

	* ∃''x''('''linguist'''(''x'') : &Square;('''like-logic'''(''x''))		* ∃''x''('''linguist'''(''x'') : &Square;('''like-logic'''(''x''))

Manfred: /* Lexical constraints */

2022-11-11T18:54:50Z

Lexical constraints

← Older revision		Revision as of 18:54, 11 November 2022
Line 105:		Line 105:

	* Modal auxiliaries:		* Modal auxiliaries:
	** Alethic ''must'': ∃''w'' (''w''=''@'' : ∀''@'' ('''ALETH'''(w,@) : α[{α'[''@'']}]))		** Alethic ''must'': ∃''w'' (''w''=''ω'' : ∀''ω'' ('''ALETH'''(''w'',''ω'') : α[{α'[''ω'']}]))

	** Deontic ''must'' with cognitive agent: ∃''w'' (''w''=''@'' : ∀''@'' ('''DEON2'''(''a'',''w'',''@'') : α[{α'[''@'',''a'']}]))		** Deontic ''must'' with cognitive agent: ∃''w'' (''w''=''ω'' : ∀''ω'' ('''DEON2'''(''a'',''w'',''ω'') : α[{α'[''ω'',''a'']}]))

	* Verbs: All verbs contribute the world variable ''@'' in their lexical entry.		* Verbs: All verbs contribute the world variable ''ω'' in their lexical entry.
	** ''call'': '''call'''(''@'',<span style="color:brown">''x''</span>)		** ''call'': '''call'''(''ω'',<span style="color:brown">''x''</span>)

	* Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.		* Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.
	** ''linguist'': <u><span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x)}]:β[x])</u>		** ''linguist'': <u><span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x)}]:β[x])</u>

Manfred: /* Example formulae */

2022-11-11T18:54:00Z

Example formulae

← Older revision		Revision as of 18:54, 11 November 2022
Line 77:		Line 77:
	== Example formulae ==		== Example formulae ==

	Sentences are translated as formulae with a free occurrence of the world variable ''@''.		Sentences are translated as formulae with a free occurrence of the world variable ''ω''.

	''Alex called.'' '''call'''(@,'''alex''') - also written as '''call'''<sub>@</sub>('''alex''')		''Alex called.'' '''call'''(''ω'','''alex''') - also written as '''call'''<sub>''ω''</sub>('''alex''')

	Modal expressions introduce an explicit quantification over worlds (modal force), where '''ACC''' is any of the accessibility relations in ''ACC''.		Modal expressions introduce an explicit quantification over worlds (modal force), where '''ACC''' is any of the accessibility relations in ''ACC''.

	Necessity modality:		Necessity modality:
	* Without cognitive agent: &Square;φ &equiv; ∃''w'' (''w''=''@'' : ∀''@'' ('''ACC'''(''w'',''@'') : φ))		* Without cognitive agent: &Square;φ &equiv; ∃''w'' (''w''=''ω'' : ∀''ω'' ('''ACC'''(''w'',''ω'') : φ))
	* With cognitive agent ''a'': &Square;<sub>''a''</sub>φ &equiv; ∃''w'' (''w''=''@'' : ∀''@'' ('''ACC'''(''a'',''w'',''@'') : φ))		* With cognitive agent ''a'': &Square;<sub>''a''</sub>φ &equiv; ∃''w'' (''w''=''ω'' : ∀''@'' ('''ACC'''(''a'',''w'',''ω'') : φ))

	Possibility modality:		Possibility modality:
	* Without cognitive agent: &Diamond;φ &equiv; ∃''w'' (''w''=''@'' : ∃''@'' ('''ACC'''(''w'',''@'') : φ))		* Without cognitive agent: &Diamond;φ &equiv; ∃''w'' (''w''=''@'' : ∃''ω'' ('''ACC'''(''w'',''ω'') : φ))
	* With cognitive agent ''a'': &Diamond;<sub>''a''</sub>φ &equiv; ∃''w'' (''w''=''@'' : ∃''@'' ('''ACC'''(''a'',''w'',''@'') : φ))		* With cognitive agent ''a'': &Diamond;<sub>''a''</sub>φ &equiv; ∃''w'' (''w''=''ω'' : ∃''ω'' ('''ACC'''(''a'',''w'',''ω'') : φ))

	Example sentences:		Example sentences:
Line 95:		Line 95:
	''A linguist necessarily likes logic.'' (deontic necessity, without cognitive agent)		''A linguist necessarily likes logic.'' (deontic necessity, without cognitive agent)
	* &Square; ∃''x''('''linguist'''(''x'') : '''like-logic'''(''x''))		* &Square; ∃''x''('''linguist'''(''x'') : '''like-logic'''(''x''))
	:: &equiv; ∃''w'' (''w''=''@'': ∀''@''('''DEON1'''(''w'',''@''): ∃''x''('''linguist'''(@,x) : '''like-logic'''(''@'',''x''))))		:: &equiv; ∃''w'' (''w''=''ω'': ∀''@''('''DEON1'''(''w'',''ω''): ∃''x''('''linguist'''(''ω'',x) : '''like-logic'''(''ω'',''x''))))

	* ∃''x''('''linguist'''(''x'') : &Square;('''like-logic'''(''x''))		* ∃''x''('''linguist'''(''x'') : &Square;('''like-logic'''(''x''))
	:: &equiv; ∃''x''('''linguist'''(@,x) : ∃''w'' (''w''=''@'': ∀''@''('''DEON1'''(''w'',''@''): '''like-logic'''(''@'',''x''))))		:: &equiv; ∃''x''('''linguist'''(''ω'',x) : ∃''w'' (''w''=''ω'': ∀''ω''('''DEON1'''(''w'',''ω''): '''like-logic'''(''ω'',''x''))))

	== Lexical constraints ==		== Lexical constraints ==

Manfred: /* Basic assumptions */

2022-11-11T18:52:12Z

Basic assumptions

← Older revision		Revision as of 18:52, 11 November 2022
Line 66:		Line 66:
	We assume:		We assume:
	* Our model contains a set of possible worlds ''W'', and a set of accessiblity relations ''ACC'', i.e. M = < ''U'', ''I'', ''W'', ''ACC'' >		* Our model contains a set of possible worlds ''W'', and a set of accessiblity relations ''ACC'', i.e. M = < ''U'', ''I'', ''W'', ''ACC'' >
	* There is a special variable, ''w''<sub>0</sub> or ''@'' that refers to the current world: [[''w''<sub>0</sub>]]<sup>M,w</sup> = w		* There is a special variable, ''w''<sub>0</sub> or ''ω'' that refers to the current world: [[''w''<sub>0</sub>]]<sup>M,w</sup> = w
	* There are special predicates for the different accessibility relations (modal bases):		* There are special predicates for the different accessibility relations (modal bases):
	** Alethic: '''ALETH'''<sub>sst</sub>		** Alethic: '''ALETH'''<sub>sst</sub>

Manfred: /* Lexical constraints */

2022-11-10T20:11:53Z

Lexical constraints

← Older revision		Revision as of 20:11, 10 November 2022
Line 113:		Line 113:

	* Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.		* Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.
	** ''linguist'': <u><span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x}]:β[x])</u>		** ''linguist'': <u><span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x)}]:β[x])</u>

Manfred: /* Lexical constraints */

2022-11-10T20:11:28Z

Lexical constraints

← Older revision		Revision as of 20:11, 10 November 2022
Line 113:		Line 113:

	* Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.		* Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.
	** ''linguist'': <span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x}]:β[x])		** ''linguist'': <u><span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x}]:β[x])</u>

Manfred: /* Lexical constraints */

2022-11-10T20:10:00Z

Lexical constraints

← Older revision		Revision as of 20:10, 10 November 2022
Line 104:		Line 104:
	'''Note:''' Non-contributed parts of formulae are marked in <span style="color:brown">brown</span>.		'''Note:''' Non-contributed parts of formulae are marked in <span style="color:brown">brown</span>.

	Alethic ''must'': ∃''w'' (''w''=''@'' : ∀''@'' ('''ALETH'''(w,@) : α[{α'[''@'']}]))		* Modal auxiliaries:
			** Alethic ''must'': ∃''w'' (''w''=''@'' : ∀''@'' ('''ALETH'''(w,@) : α[{α'[''@'']}]))

	Deontic ''must'' with cognitive agent: ∃''w'' (''w''=''@'' : ∀''@'' ('''DEON2'''(''a'',''w'',''@'') : α[{α'[''@'',''a'']}]))		** Deontic ''must'' with cognitive agent: ∃''w'' (''w''=''@'' : ∀''@'' ('''DEON2'''(''a'',''w'',''@'') : α[{α'[''@'',''a'']}]))

	Verbs: All verbs contribute the world variable ''@'' in their lexical entry.		* Verbs: All verbs contribute the world variable ''@'' in their lexical entry.
	* ''call'': '''call'''(''@'',<span style="color:brown">''x''</span>)		** ''call'': '''call'''(''@'',<span style="color:brown">''x''</span>)

	Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.		* Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.
	* ''linguist'': <span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x}]:β[x])		** ''linguist'': <span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x}]:β[x])

Manfred: /* Lexical constraints */

2022-11-10T20:08:24Z

Lexical constraints

← Older revision		Revision as of 20:08, 10 November 2022
Line 111:		Line 111:
	* ''call'': '''call'''(''@'',<span style="color:brown">''x''</span>)		* ''call'': '''call'''(''@'',<span style="color:brown">''x''</span>)

	Nouns: Nouns don't contribute their world variable. ~~The~~ constraint is that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.		Nouns: Nouns don't contribute their world variable. There is a global constraint that their world variable must be identical with ''@'' or with an other world variable in whose scope it is in the utterance.
	* ''linguist'': <span style="color:brown">Q</span>''x''(&alpha[{'''linguist'''(<span style="color:brown">''w''</span>,x}]:β[x])		* ''linguist'': <span style="color:brown">Q</span>''x''(α[{'''linguist'''(<span style="color:brown">''w''</span>,x}]:β[x])