Belief Revision in non
... logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for theories of L and iii) a classical AGM belief revision operation. In general, different translation mechanisms can be defined from a given object logic to classical logic, depending on t ...
... logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for theories of L and iii) a classical AGM belief revision operation. In general, different translation mechanisms can be defined from a given object logic to classical logic, depending on t ...
The logic of negationless mathematics
... necessary that there are at least two discernable individuals. So after adjunction of the sign #, this theory cannot be applied to a field that consists of only one individual. Formally this circumstance might be expressed by the axiom (Ex)(Ey)x # y. But this axiom is not an axiom similar to the oth ...
... necessary that there are at least two discernable individuals. So after adjunction of the sign #, this theory cannot be applied to a field that consists of only one individual. Formally this circumstance might be expressed by the axiom (Ex)(Ey)x # y. But this axiom is not an axiom similar to the oth ...
Action Logic and Pure Induction
... a∗ to be the reflexive transitive closure of a. We shall call a reflexive when 1 ≤ a and transitive when aa ≤ a, and take the reflexive transitive closure of a to be the least reflexive transitive element b such that a ≤ b. Thus the nature of this second problem is that REG has models in which a∗ is ...
... a∗ to be the reflexive transitive closure of a. We shall call a reflexive when 1 ≤ a and transitive when aa ≤ a, and take the reflexive transitive closure of a to be the least reflexive transitive element b such that a ≤ b. Thus the nature of this second problem is that REG has models in which a∗ is ...
An Overview of Intuitionistic and Linear Logic
... proof constructions), rather than validity. The study of proposition-as-type and proof normalisation form the basis of many of the functional programming languages used today. The study of proof search serves as a foundation for logic programming and leads to the discovery of new logic programming l ...
... proof constructions), rather than validity. The study of proposition-as-type and proof normalisation form the basis of many of the functional programming languages used today. The study of proof search serves as a foundation for logic programming and leads to the discovery of new logic programming l ...
Syllogistic Logic with Complements
... next turn to the proof theory. A proof tree over Γ is a finite tree T whose nodes are labeled with sentences in our fragment, with the additional property that each node is either an element of Γ or comes from its parent(s) by an application of one of the rules for the fragment listed in Figure 1. Γ ...
... next turn to the proof theory. A proof tree over Γ is a finite tree T whose nodes are labeled with sentences in our fragment, with the additional property that each node is either an element of Γ or comes from its parent(s) by an application of one of the rules for the fragment listed in Figure 1. Γ ...
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... Abiteboul and Vianu de ned another extension of FO + IFP, called FO + IFP + W, which has a nondeterministic choice operator W, called the witness operator (Abiteboul and Vianu (1991a)). This operator chooses an arbitrary element from a set given as argument. This logic is a nondeterministic logic in ...
... Abiteboul and Vianu de ned another extension of FO + IFP, called FO + IFP + W, which has a nondeterministic choice operator W, called the witness operator (Abiteboul and Vianu (1991a)). This operator chooses an arbitrary element from a set given as argument. This logic is a nondeterministic logic in ...
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... We consider two sound and complete axiomatizations for the HMS model, that differ with respect to the language used and the notion of validity. One axiomatization captures weak validity: a formula is weakly valid if it is never false (although it may be undefined). In the single-agent case, this axi ...
... We consider two sound and complete axiomatizations for the HMS model, that differ with respect to the language used and the notion of validity. One axiomatization captures weak validity: a formula is weakly valid if it is never false (although it may be undefined). In the single-agent case, this axi ...