Logic of Natural Language Semantics: Presuppositions and
... d. CIs are logically and compositionally independent of what is ‘said (in the favored sense)’, i.e. independent of the at-issue entailments. In this talk, I mainly present Potts (2005) that shows a range of different empirical phenomena such as expressive expressions, appositive nominals (ANs) or ap ...
... d. CIs are logically and compositionally independent of what is ‘said (in the favored sense)’, i.e. independent of the at-issue entailments. In this talk, I mainly present Potts (2005) that shows a range of different empirical phenomena such as expressive expressions, appositive nominals (ANs) or ap ...
Functional Programming and the Lambda Calculus
... If E 1 ↔ E 2 (are interconvertable), then there exists an E such that E 1 → E and E 2 → E . “Reduction in any way can eventually produce the same result.” If E 1 → E 2 , and E 2 is is normal form, then there is a normal-order reduction of E 1 to E 2 . “Normal-order reduction will always produce a no ...
... If E 1 ↔ E 2 (are interconvertable), then there exists an E such that E 1 → E and E 2 → E . “Reduction in any way can eventually produce the same result.” If E 1 → E 2 , and E 2 is is normal form, then there is a normal-order reduction of E 1 to E 2 . “Normal-order reduction will always produce a no ...
Intuitionistic Logic
... Intuitionism is an approach to the philosophy of mathematics and to mathematical practice pioneered by L. E. J. Brouwer. The central thesis of intuitionism is that mathematics has as its subject matter mental mathematical constructions. If they were all finite, then classical reasoning would be adeq ...
... Intuitionism is an approach to the philosophy of mathematics and to mathematical practice pioneered by L. E. J. Brouwer. The central thesis of intuitionism is that mathematics has as its subject matter mental mathematical constructions. If they were all finite, then classical reasoning would be adeq ...
predicate
... • ⊨ holds iff for all models M and lookup tables l, whenever M ⊨l holds for all then M ⊨l holds as well • is satisfiable iff there is some model M and lookup table l such that M ⊨l holds • is valid iff M ⊨l holds for all models M and lookup tables l ...
... • ⊨ holds iff for all models M and lookup tables l, whenever M ⊨l holds for all then M ⊨l holds as well • is satisfiable iff there is some model M and lookup table l such that M ⊨l holds • is valid iff M ⊨l holds for all models M and lookup tables l ...
crooks
... Large pad-over-logic pad cells for bump-bond tests LVDS receiver and transmitter pad circuits Gray code counter for timestamp generation Clock generator (makes all sensor internal clocks from one external clock) Bunch train state machine Readout state machine Master controller (co-ordinates precedin ...
... Large pad-over-logic pad cells for bump-bond tests LVDS receiver and transmitter pad circuits Gray code counter for timestamp generation Clock generator (makes all sensor internal clocks from one external clock) Bunch train state machine Readout state machine Master controller (co-ordinates precedin ...
(A B) |– A
... Grundzüge der theoretischen Logik, in which they arrived at exactly this point: they had defined axioms and derivation rules of predicate logic (slightly distinct from the above), and formulated the problem of completeness. They raised a question whether such a proof calculus is complete in the sens ...
... Grundzüge der theoretischen Logik, in which they arrived at exactly this point: they had defined axioms and derivation rules of predicate logic (slightly distinct from the above), and formulated the problem of completeness. They raised a question whether such a proof calculus is complete in the sens ...
Proof Theory - Andrew.cmu.edu
... I will assume the reader is familiar with the language of first-order logic. Contemporary logic textbooks often present formal calculi for first-order logic with a long list of axioms and a few simple rules, but these are generally not very convenient for modeling deductive arguments or studying the ...
... I will assume the reader is familiar with the language of first-order logic. Contemporary logic textbooks often present formal calculi for first-order logic with a long list of axioms and a few simple rules, but these are generally not very convenient for modeling deductive arguments or studying the ...
Logic I Fall 2009 Problem Set 5
... Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete iff a language with ...
... Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete iff a language with ...
Mathematical Logic
... Abduction/Induction: given a theory T and an observation φ, find an explanation Γ such that T ∪ Γ |= φ Satisfiability Checking: given a set of formulae Γ, check whether there exists a model I such that I |= φ for all φ ∈ Γ? Model Checking: given a model I and a formula φ, check whether I|=φ Automate ...
... Abduction/Induction: given a theory T and an observation φ, find an explanation Γ such that T ∪ Γ |= φ Satisfiability Checking: given a set of formulae Γ, check whether there exists a model I such that I |= φ for all φ ∈ Γ? Model Checking: given a model I and a formula φ, check whether I|=φ Automate ...
.pdf
... Substitution A|pB is the replacement of all occurrences of the variable p in A by the formula B. There are a few issues, however, that one needs to be aware of. Variables that are bound by a quantifier, must not be replaced, as this would change the meaning. ((∃p)(p⊃∼q))|qp should not result in ((∃p ...
... Substitution A|pB is the replacement of all occurrences of the variable p in A by the formula B. There are a few issues, however, that one needs to be aware of. Variables that are bound by a quantifier, must not be replaced, as this would change the meaning. ((∃p)(p⊃∼q))|qp should not result in ((∃p ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.