1. (SYNTAX-DRIVEN) SEMANTICS Yılmaz Kılıçaslan

2. Outline  Semiotic Triangle –Syntax –Semantics –Pragmatics  (Syntax-driven) Semantics –Semantics via languages of logic –Model-based semantics –Lambda-calculus  Computational Issues –Coding the semantic value of basic expressions –Handling the lambda operator –Implementing compositionality with lambda calculus 2

3. Semiotic Triangle Ogden and Richard’s Semiotic Triangle The three branches of semiotics: syntactics (syntax)—how signs relate to other signs (example: how the word “dog” relates to the other words in the sentence “The dog ate my homework.”) semantics—study of how signs relate to things (example: how the word “dog” relates to an actual dog) pragmatics—actual use of codes in everyday life; effects of signs on human behavior and how people mold signs and meanings in their actual interaction (example: How would the sentence “The dog ate my homework” be used in everyday life? How would my teacher react to it?)

4. A Formal Language for First-Order Logic 4 S YNTAX: M ODEL: For  Pred1(Term) For  Pred2(Term, Term) For  [For Con For] For   For For  Quant Var For Con   Quant   |  Pred1  S Pred2  L Term  Name Term  Var Name  j | k | v | m Var  x | y | z | x 1 |... A = {a, b, c} S EMANTICS: (Ignoring Quantification) M = F(j) = a F(v) = c F(k) = b F(m) = c 0101 1010 [  ] M = abcabc 0101 F(S) = F(L) = abcabc abcabc 0101 abcabc 0101 abcabc 0101 0101 0101 0101 [  ] M = 0101 0101 Example : [  [L(j, k)]] M = [  ] M ([L(j, k)]] M ) = [  ] M ([F(L)(F(k))](F(j))) = [  ] M ([F(L)(b)](a)) = [  ] M (0) = 1 [Pred1(α)] M = F(Pred1)(F(Term)) [Pred2(α,β)] M = [F(Pred2)(F(β))](F(α)) [F1  F2] M = [[  ] M ([F1] M )]([F2] M ) [  F] M = [  ] M ([F] M )

5. Natural Language Semantics in FOL 5 Compositional Translation: Example: ̏ John loves Katy ̋ S N VP NV John lovesKaty y xL(x,y) k j xL(x,k) L(j,k)

6. A Fatal Problem with Semantics in FOL 6 Referentially Opaque Constructions: i.e. constructions creating contexts where Leibnitz’ Law fails. The result of substituting in any formula one name for another name denoting the same individual results in a formula that is true iff the original formula was true Example: (a) ̏ John believes that the Morning Star is the Morning Star. ̋ (b) ̏ John believes that the Morning Star is Venus. ̋ [m] M = [v] M = c ⇒ [B(j, m = m)] M = [B(j, m = v)] M But, (b) might be false while (a) is true. B(j, m = m) B(j, m = v)

7. Intensional Logic (IL) A Platonic View of Reality 7 A = {a,b,c,d} W = {w 1,w 2 } M = F(v) = w1w2w1w2 cccc F(m) = w1w2w1w2 cdcd F(j) = aaaa w1w2w1w2 Plato’s Ideas Kripke’s Possible Worlds Carnap’s Intensions Frege’s Senses Montague’s Intensional Logic S YNTAX: S EMANTICS: M ODEL:... For  (Term = Term)... Expr  ^Expr... [^α] M = w 1... w N [α] M,w 1 [α] M,w N [α = β] M,w = 1 ⇔ [α] M,w = [β] M,w Example : [^(m = m)] M = w1w2w1w2 1111 [^(m = v)] M = w1w2w1w2 1010

8. Natural Language Semantics in IL De Dicto Readings: (a) ̏ John believes that the Morning Star is the Morning Star. ̋ (b) ̏ John believes that the Morning Star is Venus. ̋ Translations into IL: B(j, ^(m = m)) B(j, ^(m = v)) A De Re Reading: ̏ John believes that the Morning Star is Venus. ̋ x[B(j, ^(x = v))](m) (b) can be false while (a) is true. [^(m = m)] M As ≠ [^(m = v)] M

9. Problems with Possible Worlds Semantics 9 Logically Equivalent Sentences : If two sentences  and  are logically equivalent, then it will always be a logically valid inference from B(α, ^  ) to B(α, ^  ), for any believer denoted by α. However, a person might believe a sentence without believing its equivalent.

10. Conclusion 10 Using formal languages of logic as a bridge, we can develop a truth-conditional, model-theoretic natural language semantics adhering to the principle of compositionality. However, this approach ultimately fails (e.g. in the case of logically equivalent sentences in opaque contexts).