Introduction to Linear Logic
... For pedagogical purposes we shall also have a look at Classical Logic as well as Intuitionistic Logic. Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control. The focus of ...
... For pedagogical purposes we shall also have a look at Classical Logic as well as Intuitionistic Logic. Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control. The focus of ...
Formal deduction in propositional logic
... • Remark: In (∨−) it is the ∨ between A and B in A ∨ B that is eliminated in the conclusion C . • (¬ −) expresses the method of indirect proof or proof by contradiction: if a contradiction (denoted by B and ¬B) follows from certain premises (denoted by Σ) with an additional supposition that a certai ...
... • Remark: In (∨−) it is the ∨ between A and B in A ∨ B that is eliminated in the conclusion C . • (¬ −) expresses the method of indirect proof or proof by contradiction: if a contradiction (denoted by B and ¬B) follows from certain premises (denoted by Σ) with an additional supposition that a certai ...
In order to define the notion of proof rigorously, we would have to
... discharging mechanism but they all involve some form of tagging (with “new” variable). For example, the rule formalizing the process that we have just described to prove an implication, A ⇒ B, known as ⇒-introduction, uses a tagging mechanism described precisely in Definition 1.2.1. Now, the rule th ...
... discharging mechanism but they all involve some form of tagging (with “new” variable). For example, the rule formalizing the process that we have just described to prove an implication, A ⇒ B, known as ⇒-introduction, uses a tagging mechanism described precisely in Definition 1.2.1. Now, the rule th ...
notes
... The rst is valid if and only if the assertion P is valid while the second is valid if and only if the command c does not halt. It turns out that the culprit is the C rule, C ...
... The rst is valid if and only if the assertion P is valid while the second is valid if and only if the command c does not halt. It turns out that the culprit is the C rule, C ...
Proofs in Propositional Logic
... This tactic can be useful for avoiding proof duplication inside some interactive proof. Notice that the scope of the declaration H :B is limited to the second subgoal. If a proof of B is needed elsewhere, it would be better to prove a lemma stating B. Remark : Sometimes the overuse of assert may lea ...
... This tactic can be useful for avoiding proof duplication inside some interactive proof. Notice that the scope of the declaration H :B is limited to the second subgoal. If a proof of B is needed elsewhere, it would be better to prove a lemma stating B. Remark : Sometimes the overuse of assert may lea ...
A Computationally-Discovered Simplification of the Ontological
... Following the example of Fitelson and Zalta [2007], we investigated the above analysis with the help of automated reasoning technologies. We implemented our 1991 formulation of the ontological argument in prover9, which is a well-known and easy-to-use theorem-proving environment. In what follows, we ...
... Following the example of Fitelson and Zalta [2007], we investigated the above analysis with the help of automated reasoning technologies. We implemented our 1991 formulation of the ontological argument in prover9, which is a well-known and easy-to-use theorem-proving environment. In what follows, we ...
Sequent-Systems for Modal Logic
... All rules for logical constants will be given by double-line rules. Then we shall present sequent-systems for classical, Heyting and KolmogorovJohansson ("minimal") propositional logic, and also a sequent-system for an intuitionistic relevant propositional logic, which is essentially logic without T ...
... All rules for logical constants will be given by double-line rules. Then we shall present sequent-systems for classical, Heyting and KolmogorovJohansson ("minimal") propositional logic, and also a sequent-system for an intuitionistic relevant propositional logic, which is essentially logic without T ...