Strong Completeness and Limited Canonicity for PDL
... i.e. when | ϕ implies that there is a finite ⊆ with | ϕ, hence | → ϕ. This is, for example, the case in propositional and predicate logic, and in many modal logics such as K and S5. Segerberg’s axiomatization of PDL is only weakly complete, since PDL is not compact: we have that {[a ...
... i.e. when | ϕ implies that there is a finite ⊆ with | ϕ, hence | → ϕ. This is, for example, the case in propositional and predicate logic, and in many modal logics such as K and S5. Segerberg’s axiomatization of PDL is only weakly complete, since PDL is not compact: we have that {[a ...
The logic of negationless mathematics
... But in negationless logic this derivation is only possible, if it is known that p A r exists. Therefore the premiss ~vs. p A r has to be added. From this example it is seen that in many cases additional premisses of the form ~vs p will distinguish the present calculus from the usual logical calculi. ...
... But in negationless logic this derivation is only possible, if it is known that p A r exists. Therefore the premiss ~vs. p A r has to be added. From this example it is seen that in many cases additional premisses of the form ~vs p will distinguish the present calculus from the usual logical calculi. ...
Clauses Versus Gates in CEGAR-Based 2QBF Solving Valeriy Balabanov, Jie-Hong R. Jiang,
... E.g., in (Mishchenko et al. 2015) FPGA synthesis benchmarks are formulated on And-Inverter graphs (AIGs), which is an efficient way to represent general Boolean networks. It is known that any Boolean circuit can be transformed into an equisatisfiable CNF formula, by the various CNFization procedures ...
... E.g., in (Mishchenko et al. 2015) FPGA synthesis benchmarks are formulated on And-Inverter graphs (AIGs), which is an efficient way to represent general Boolean networks. It is known that any Boolean circuit can be transformed into an equisatisfiable CNF formula, by the various CNFization procedures ...
Glivenko sequent classes in the light of structural proof theory
... defined in terms of absence of certain logical constants in the positive or negative parts of sequents. For five of the seven classes the results are strengthened to height-preserving statements; for them, we do not give proof transformations but actually show that, with the appropriate calculus, th ...
... defined in terms of absence of certain logical constants in the positive or negative parts of sequents. For five of the seven classes the results are strengthened to height-preserving statements; for them, we do not give proof transformations but actually show that, with the appropriate calculus, th ...
Relational Theories with Null Values and Non-Herbrand
... By Π∆,Σ we denote the conjunction of Π∆ with DCA and with all unique name axioms from T∆,Σ (that is to say, with all unique name axioms except for the optional axioms that do not belong to Σ). The following theorem expresses the soundness of this translation: Theorem 2. For any set ∆ of positive gro ...
... By Π∆,Σ we denote the conjunction of Π∆ with DCA and with all unique name axioms from T∆,Σ (that is to say, with all unique name axioms except for the optional axioms that do not belong to Σ). The following theorem expresses the soundness of this translation: Theorem 2. For any set ∆ of positive gro ...
A Simple Tableau System for the Logic of Elsewhere
... the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense ...
... the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense ...
POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
... Now, Kaplan’s argument shows that the principle of plenitude is incompatible with assumptions commonly made in possible worlds semantics. Here is how the argument goes: (i) There is a set W of possible worlds and a set P rop of propositions. (ii) There is, for every subset X of W , a corresponding p ...
Beginning Logic - University of Notre Dame
... All Notre Dame women are smart. Susan is a Notre Dame woman. Therefore, Susan is smart. The second argument has the same form as the first. If we agree that the first argument is valid, then we should believe the second as well. As tools for analyzing arguments, we will develop formal languages, a f ...
... All Notre Dame women are smart. Susan is a Notre Dame woman. Therefore, Susan is smart. The second argument has the same form as the first. If we agree that the first argument is valid, then we should believe the second as well. As tools for analyzing arguments, we will develop formal languages, a f ...
