Compositionality Tutorial 4 Pros and Cons Dag Westerst˚ahl Stockholm University and University of Gothenburg Tsinghua University, Beijing June 17, 2011 Tsinghua University, Beijing June 17, 2011 1 Dag Westerst˚ahl () Compositionality 4 / 20 Outline 1 Denials Denial 1: \X is not compositional" Denial 2: ambiguity Denial 3: idioms Conclusions 2 Emptiness 3 Praise Tsinghua University, Beijing June 17, 2011 2 Dag Westerst˚ahl () Compositionality 4 / 20 Yes: FO is not compositional if semantic values are truth values and assignments are seen as parameters. (Because assignments are shifted in the clauses for the quantifiers.) But FO is compositional if semantic values are sets of assignments. X = Independence-Friendly logic (Hintikka, who explicitly makes the non-compositionality claim). Yes: It can be shown that no semantics for IF-logic which takes sets of assignments as values can be compositional (Cameron and Hodges). No: We already saw (Hodges' extension theorem) that compositional semantics with certain nice properties exist. Moreover, an interesting compositional semantics which takes semantic values to be sets of sets of assignments (so-called trumps or teams) has been given by Hodges (see V¨a¨an¨anen, Dependence Logic, 2007). Denials Denial 1: \X is not compositional" \X is not compositional" X = first-order logic: 1 of 20 But FO is compositional if semantic values are sets of assignments. X = Independence-Friendly logic (Hintikka, who explicitly makes the non-compositionality claim). Yes: It can be shown that no semantics for IF-logic which takes sets of assignments as values can be compositional (Cameron and Hodges). No: We already saw (Hodges' extension theorem) that compositional semantics with certain nice properties exist. Moreover, an interesting compositional semantics which takes semantic values to be sets of sets of assignments (so-called trumps or teams) has been given by Hodges (see V¨a¨an¨anen, Dependence Logic, 2007). Denials Denial 1: \X is not compositional" \X is not compositional" X = first-order logic: Yes: FO is not compositional if semantic values are truth values and assignments are seen as parameters. (Because assignments are shifted in the clauses for the quantifiers.) 1 of 20 X = Independence-Friendly logic (Hintikka, who explicitly makes the non-compositionality claim). Yes: It can be shown that no semantics for IF-logic which takes sets of assignments as values can be compositional (Cameron and Hodges). No: We already saw (Hodges' extension theorem) that compositional semantics with certain nice properties exist. Moreover, an interesting compositional semantics which takes semantic values to be sets of sets of assignments (so-called trumps or teams) has been given by Hodges (see V¨a¨an¨anen, Dependence Logic, 2007). Denials Denial 1: \X is not compositional" \X is not compositional" X = first-order logic: Yes: FO is not compositional if semantic values are truth values and assignments are seen as parameters. (Because assignments are shifted in the clauses for the quantifiers.) But FO is compositional if semantic values are sets of assignments. 1 of 20 Yes: It can be shown that no semantics for IF-logic which takes sets of assignments as values can be compositional (Cameron and Hodges). No: We already saw (Hodges' extension theorem) that compositional semantics with certain nice properties exist. Moreover, an interesting compositional semantics which takes semantic values to be sets of sets of assignments (so-called trumps or teams) has been given by Hodges (see V¨a¨an¨anen, Dependence Logic, 2007). Denials Denial 1: \X is not compositional" \X is not compositional" X = first-order logic: Yes: FO is not compositional if semantic values are truth values and assignments are seen as parameters. (Because assignments are shifted in the clauses for the quantifiers.) But FO is compositional if semantic values are sets of assignments. X = Independence-Friendly logic (Hintikka, who explicitly makes the non-compositionality claim). 1 of 20 No: We already saw (Hodges' extension theorem) that compositional semantics with certain nice properties exist. Moreover, an interesting compositional semantics which takes semantic values to be sets of sets of assignments (so-called trumps or teams) has been given by Hodges (see V¨a¨an¨anen, Dependence Logic, 2007). Denials Denial 1: \X is not compositional" \X is not compositional" X = first-order logic: Yes: FO is not compositional if semantic values are truth values and assignments are seen as parameters. (Because assignments are shifted in the clauses for the quantifiers.) But FO is compositional if semantic values are sets of assignments. X = Independence-Friendly logic (Hintikka, who explicitly makes the non-compositionality claim). Yes: It can be shown that no semantics for IF-logic which takes sets of assignments as values can be compositional (Cameron and Hodges). 1 of 20 Moreover, an interesting compositional semantics which takes semantic values to be sets of sets of assignments (so-called trumps or teams) has been given by Hodges (see V¨a¨an¨anen, Dependence Logic, 2007). Denials Denial 1: \X is not compositional" \X is not compositional" X = first-order logic: Yes: FO is not compositional if semantic values are truth values and assignments are seen as parameters. (Because assignments are shifted in the clauses for the quantifiers.) But FO is compositional if semantic values are sets of assignments. X = Independence-Friendly logic (Hintikka, who explicitly makes the non-compositionality claim). Yes: It can be shown that no semantics for IF-logic which takes sets of assignments as values can be compositional (Cameron and Hodges). No: We already saw (Hodges' extension theorem) that compositional semantics with certain nice properties exist. 1 of 20 Denials Denial 1: \X is not compositional" \X is not compositional" X = first-order logic: Yes: FO is not compositional if semantic values are truth values and assignments are seen as parameters. (Because assignments are shifted in the clauses for the quantifiers.) But FO is compositional if semantic values are sets of assignments. X = Independence-Friendly logic (Hintikka, who explicitly makes the non-compositionality claim). Yes: It can be shown that no semantics for IF-logic which takes sets of assignments as values can be compositional (Cameron and Hodges). No: We already saw (Hodges' extension theorem) that compositional semantics with certain nice properties exist. Moreover, an interesting compositional semantics which takes semantic values to be sets of sets of assignments (so-called trumps or teams) has been given by Hodges (see V¨a¨an¨anen, Dependence Logic, 2007). 1 of 20 This is too unspecified. Compositionality is relative to a syntactic analysis (a grammar) and an assignment of semantic values. X = English belief sentences, of the form \A believes that '": This is more interesting: If extensions are semantic values, and (1) Karl believes that Mark Twain is a novelist. (2) Karl believes that Samuel Clemens is a novelist. can differ in truth value, and if truth value depends on semantic value, then the semantics for (this fragment of) English is not compositional. Also, if intensions are semantic values, and (3) Karl believes that Mark Twain is a novelist. (4) Karl believes that Mark Twain is a novelist and 172 = 289. can differ in truth value, and if truth value depends on semantic value, then the semantics for (this fragment of) English is not compositional. Denials Denial 1: \X is not compositional" \X is not compositional", cont. X = English: 2 of 20 X = English belief sentences, of the form \A believes that '": This is more interesting: If extensions are semantic values, and (1) Karl believes that Mark Twain is a novelist. (2) Karl believes that Samuel Clemens is a novelist. can differ in truth value, and if truth value depends on semantic value, then the semantics for (this fragment of) English is not compositional. Also, if intensions are semantic values, and (3) Karl believes that Mark Twain is a novelist. (4) Karl believes that Mark Twain is a novelist and 172 = 289. can differ in truth value, and if truth value depends on semantic value, then the semantics for (this fragment of) English is not compositional. Denials Denial 1: \X is not compositional" \X is not compositional", cont. X = English: This is too unspecified. Compositionality is relative to a syntactic analysis (a grammar) and an assignment of semantic values. 2 of 20 This is more interesting: If extensions are semantic values, and (1) Karl believes that Mark Twain is a novelist. (2) Karl believes that Samuel Clemens is a novelist. can differ in truth value, and if truth value depends on semantic value, then the semantics for (this fragment of) English is not compositional. Also, if intensions are semantic values, and (3) Karl believes that Mark Twain is a novelist. (4) Karl believes that Mark Twain is a novelist and 172 = 289. can differ in truth value, and if truth value depends on semantic value, then the semantics for (this fragment of) English is not compositional. Denials Denial 1: \X is not compositional" \X is not compositional", cont. X = English: This is too unspecified. Compositionality is relative to a syntactic analysis (a grammar) and an assignment of semantic values. X = English belief sentences, of the form \A believes that '": 2 of 20 Also, if intensions are semantic values, and (3) Karl believes that Mark Twain is a novelist. (4) Karl believes that Mark Twain is a novelist and 172 = 289. can differ in truth value, and if truth value depends on semantic value, then the semantics for (this fragment of) English is not compositional. Denials Denial 1: \X is not compositional" \X is not compositional", cont. X = English: This is too unspecified. Compositionality is relative to a syntactic analysis (a grammar) and an assignment of semantic values. X = English belief sentences, of the form \A believes that '": This is more interesting: If extensions are semantic values, and (1) Karl believes that Mark Twain is a novelist.