Proof theory for modal logic
... sign). For S5 also negations of modal formulas are allowed among the assumptions. The necessitation rule is regarded as the introduction rule for 2, whereas the elimination rule is simply 2A/A. Although “natural,” the system is not normalizable, as there are non-eliminable detours. Prawitz introduce ...
... sign). For S5 also negations of modal formulas are allowed among the assumptions. The necessitation rule is regarded as the introduction rule for 2, whereas the elimination rule is simply 2A/A. Although “natural,” the system is not normalizable, as there are non-eliminable detours. Prawitz introduce ...
The Development of Categorical Logic
... construction of the usual cumulative hierarchy of sets generated by a collection of atoms can be carried out within a locally small complete topos E (in particular, any Grothendieck topos). This leads to a topos E*—in a certain sense a well-founded part of E—which is a model of IZF with atoms. By st ...
... construction of the usual cumulative hierarchy of sets generated by a collection of atoms can be carried out within a locally small complete topos E (in particular, any Grothendieck topos). This leads to a topos E*—in a certain sense a well-founded part of E—which is a model of IZF with atoms. By st ...
Chapter 9: Initial Theorems about Axiom System AS1
... the conditional connective of the object language. When we translate ‘„’ as ‘is a theorem’, we obtain: if α is a theorem, and α→β is a theorem, then β is a theorem. The informal proof of (T4) goes as follows. Proof: Suppose „α and „α→β, to show „β. Then, α and α→β are provable; so there is a proof o ...
... the conditional connective of the object language. When we translate ‘„’ as ‘is a theorem’, we obtain: if α is a theorem, and α→β is a theorem, then β is a theorem. The informal proof of (T4) goes as follows. Proof: Suppose „α and „α→β, to show „β. Then, α and α→β are provable; so there is a proof o ...
Sets
... Boolean data type If statement Impact of negations Implementation of quantifiers Discrete Mathematical Structures: Theory and Applications ...
... Boolean data type If statement Impact of negations Implementation of quantifiers Discrete Mathematical Structures: Theory and Applications ...
Document
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
propositions and connectives propositions and connectives
... connectives – each has one or more meanings in natural language – need for precise, formal language ...
... connectives – each has one or more meanings in natural language – need for precise, formal language ...
Inductive-Deductive Reasoning
... Subtract the original number: Result: Now Prove it Using Deductive Reasoning! ...
... Subtract the original number: Result: Now Prove it Using Deductive Reasoning! ...
Frege, Boolos, and Logical Objects
... Frege’s plan in the Grundlagen and Grundgesetze.4 Boolos notes that the explicit assertion of the existence of numbers embodied by Numbers is a way of making clear the commitment implicit in the use of the definite article in ‘the number of F s’.5 In his papers of [1986] and [1993], Boolos returned t ...
... Frege’s plan in the Grundlagen and Grundgesetze.4 Boolos notes that the explicit assertion of the existence of numbers embodied by Numbers is a way of making clear the commitment implicit in the use of the definite article in ‘the number of F s’.5 In his papers of [1986] and [1993], Boolos returned t ...
