Exercise Semantics of Predicate Logic - Revision history

Manfred: /* Interpretation of atomic formulae */

2015-04-14T08:01:51Z

Interpretation of atomic formulae

← Older revision		Revision as of 08:01, 14 April 2015
Line 3:		Line 3:
	Interpret the following formulae as true or false. If you have not defined these relations or properties in your model use the ones given in [[ExerciseFOModels-d\|a previous exercise]].		Interpret the following formulae as true or false. If you have not defined these relations or properties in your model use the ones given in [[ExerciseFOModels-d\|a previous exercise]].

	* '''father-of-someone'''('''paul''','''~~Lisa~~''')		* '''father-of-someone'''('''paul''','''lisa''')
	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
	Check your answers		Check your answers

Manfred: /* Interpretation of atomic formulae */

2014-05-07T01:36:54Z

Interpretation of atomic formulae

Manfred: /* Interpretation of atomic formulae */

2014-05-07T01:35:49Z

Interpretation of atomic formulae

← Older revision		Revision as of 01:35, 7 May 2014
Line 8:		Line 8:
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />		<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />
			< <nowiki>[[</nowiki>'''paul''']], <nowiki>[[</nowiki>'''lisa''']] ∈ <nowiki>[[</nowiki>'''father-of-someone''']] iff<br />
	< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />		< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
	< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.		< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.

Manfred: /* Interpretation of atomic formulae */

2014-05-07T01:33:56Z

Interpretation of atomic formulae

← Older revision		Revision as of 01:33, 7 May 2014
Line 7:		Line 7:
	Check your answers		Check your answers
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	[['''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />		<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />
	< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />		< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
	< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.		< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.

Manfred: /* Interpretation of atomic formulae */

2014-05-07T01:33:33Z

Interpretation of atomic formulae

← Older revision		Revision as of 01:33, 7 May 2014
Line 7:		Line 7:
	Check your answers		Check your answers
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	'''father-of-someone'''('''paul''','''lisa''') = ''true'' iff<br />		[['''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />
	< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />		< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
	< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.		< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.

Suzanne: /* Interpretation of formulae with logical connectives */

2014-01-06T21:04:45Z

Interpretation of formulae with logical connectives

← Older revision		Revision as of 21:04, 6 January 2014
Line 107:		Line 107:

	'''Disjunction (v)''': At least one of the atomic formulae has to be true in order for the complex formula to be true.		'''Disjunction (v)''': At least one of the atomic formulae has to be true in order for the complex formula to be true.


	</div>		</div>
	</div>		</div>

Suzanne: /* Interpretation of formulae with logical connectives */

2014-01-06T21:04:17Z

Interpretation of formulae with logical connectives

← Older revision		Revision as of 21:04, 6 January 2014
Line 82:		Line 82:
	'''b.)''' Tom is not Paul's daughter or Tom is tall.		'''b.)''' Tom is not Paul's daughter or Tom is tall.

	'''[[~~AnswerEX3~~-~~b\|Check your solution~~]]'''		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
			Check your answers
			<div class="mw-collapsible-content">
			Sentence: Tom is not Paul's daughter or Tom is tall.


			Here the interpretation in predicate logic notation:


			<nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul) v tall(Tom)''']] = ''true'' <br/>


			because <nowiki>[[</nowiki>'''¬daughter-of-someone (Tom,Paul)''']]= ''true'' <br/>


			::because I('''Tom''')= <''Tom''>, I('''Paul''')= <''Paul''> and <''Tom,Paul''> is NOT in the set of I('''daughter-of-someone''') <br/>


			and <nowiki>[[</nowiki>'''tall(Tom)''']] = ''false'' <br/>


			::because I('''Tom''')= <''Tom''> and <''Tom''> is NOT an element of I('''tall'''). <br/>


			'''Disjunction (v)''': At least one of the atomic formulae has to be true in order for the complex formula to be true.


			</div>
			</div>

Suzanne: /* Interpretation of formulae with logical connectives */

2014-01-06T21:03:23Z

Interpretation of formulae with logical connectives

← Older revision		Revision as of 21:03, 6 January 2014
Line 52:		Line 52:
	'''a.)''' Alice is a dog and Lisa and Tom enjoy watching football together.		'''a.)''' Alice is a dog and Lisa and Tom enjoy watching football together.

	'''[[~~AnswerEX3~~-~~a\|Check your solution~~]]'''		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
			Check your answers
			<div class="mw-collapsible-content">Sentence: Alice is a dog and Lisa and Tom enjoy watching football together.


			Here the interpretation in predicate logic notation:


			<nowiki>[[</nowiki>'''dog (Alice) Ʌ enjoy-watching-football-together (Lisa,Tom)''']] = ''false''<br/>


			because <nowiki>[[</nowiki>'''dog (Alice)''']]= ''false'' <br/>


			::because I('''Alice''')= <''Alice''> and <''Alice''> is NOT an element of I('''dog''') <br/>


			and <nowiki>[[</nowiki>'''enjoy-watching-soccer-together (Lisa,Tom)''']] = ''true'' <br/>


			::because I('''Lisa''')= <''Lisa''>, I('''Tom''')= <''Tom''> and <''Lisa,Tom''> '''is''' in the set of I('''enjoy-watching-football-together'''). <br/>


			'''Conjunction (Ʌ)''': Both atomic formulae have to be true in order for the complex formula to be true.
			</div>
			</div>

Suzanne: /* Interpretation of atomic formulae */

2014-01-06T21:02:19Z

Interpretation of atomic formulae

← Older revision		Revision as of 21:02, 6 January 2014
Line 6:		Line 6:
	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
	Check your answers		Check your answers
	<div class="mw-collapsible-content">{~~{Lorem}~~}</div>		<div class="mw-collapsible-content">
			'''father-of-someone'''('''paul''','''lisa''') = ''true'' iff<br />
			< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
			< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.

			Since this is the case, the formula is true.
			</div>
	</div>		</div>

Line 14:		Line 20:
	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
	Check your answers		Check your answers
	<div class="mw-collapsible-content">{~~{Lorem}~~}</div>		<div class="mw-collapsible-content">
			'''blonde(walter)''' = ''true'' iff<br />
			< I('''walter''') > ∈ I('''blonde''') iff <br />
			< ''Walter'' > ∈ {< ''Alice'' >,< ''Lisa'' >}.

			Since this is not the case, the overall formula is false.
			</div>
	</div>		</div>

Line 22:		Line 34:
	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
	Check your answers		Check your answers
	<div class="mw-collapsible-content">{~~{Lorem}~~}</div>		<div class="mw-collapsible-content">
			'''enjoy-watching-football-togehter(alice,tom)''' = ''true'' iff<br />
			< I('''alice'''), I('''tom''') > ∈ I('''enjoy-watching-football-together''') iff<br />
			< ''Alice'', ''Tom'' > ∈ {<''Alice, Paul''>,<''Paul, Alice''>,<''Alice, Lisa''>,<''Lisa, Alice''>,<''Alice, Tom''>,<''Tom, Alice''>,<''Paul, Lisa''>,<''Lisa, Paul''>,<''Paul, Tom''>,<''Tom, Paul''>,<''Tom, Lisa''>,<''Lisa, Tom''>}

			Since this is the case, the formula is true.

			</div>
	</div>		</div>
	<br/>		<br/>

Suzanne: /* Interpretation of atomic formulae */

2014-01-06T21:01:06Z

Interpretation of atomic formulae

← Older revision		Revision as of 21:01, 6 January 2014
Line 24:		Line 24:
	<div class="mw-collapsible-content">{{Lorem}}</div>		<div class="mw-collapsible-content">{{Lorem}}</div>
	</div>		</div>
			<br/>
			<br/>

	== Interpretation of formulae with logical connectives ==		== Interpretation of formulae with logical connectives ==

← Older revision		Revision as of 01:36, 7 May 2014
Line 8:		Line 8:
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />		<nowiki>[[</nowiki>'''father-of-someone'''('''paul''','''lisa''')]] = ''true'' iff<br />
	< <nowiki>[[</nowiki>'''paul''']], <nowiki>[[</nowiki>'''lisa''']] ∈ <nowiki>[[</nowiki>'''father-of-someone''']] iff<br />		< <nowiki>[[</nowiki>'''paul''']], <nowiki>[[</nowiki>'''lisa''']] > ∈ <nowiki>[[</nowiki>'''father-of-someone''']] iff<br />
	< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />		< I('''paul'''), I('''lisa''') > ∈ I('''father-of-someone''') iff<br />
	< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.		< ''Paul'', ''Lisa''> ∈ {<''Paul, Tom''>,<''Paul, Lisa''>}.
Line 22:		Line 22:
	Check your answers		Check your answers
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	'''blonde(walter)''' = ''true'' iff<br />		<nowiki>[[</nowiki>'''blonde(walter)''']] = ''true'' iff<br />
	< I('''walter''') > ∈ I('''blonde''') iff <br />		< I('''walter''') > ∈ I('''blonde''') iff <br />
	< ''Walter'' > ∈ {< ''Alice'' >,< ''Lisa'' >}.		< ''Walter'' > ∈ {< ''Alice'' >,< ''Lisa'' >}.
Line 36:		Line 36:
	Check your answers		Check your answers
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	'''enjoy-watching-football-togehter(alice,tom)''' = ''true'' iff<br />		<nowiki>[[</nowiki>'''enjoy-watching-football-togehter(alice,tom)''']] = ''true'' iff<br />
	< I('''alice'''), I('''tom''') > ∈ I('''enjoy-watching-football-together''') iff<br />		< I('''alice'''), I('''tom''') > ∈ I('''enjoy-watching-football-together''') iff<br />
	< ''Alice'', ''Tom'' > ∈ {<''Alice, Paul''>,<''Paul, Alice''>,<''Alice, Lisa''>,<''Lisa, Alice''>,<''Alice, Tom''>,<''Tom, Alice''>,<''Paul, Lisa''>,<''Lisa, Paul''>,<''Paul, Tom''>,<''Tom, Paul''>,<''Tom, Lisa''>,<''Lisa, Tom''>}		< ''Alice'', ''Tom'' > ∈ {<''Alice, Paul''>,<''Paul, Alice''>,<''Alice, Lisa''>,<''Lisa, Alice''>,<''Alice, Tom''>,<''Tom, Alice''>,<''Paul, Lisa''>,<''Lisa, Paul''>,<''Paul, Tom''>,<''Tom, Paul''>,<''Tom, Lisa''>,<''Lisa, Tom''>}