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... formula is evaluated to true if and only if the root node of the formula is evaluated to true. In order to determine the value of this node given by an interpretation, one may compute the value of each node in reverse topological order; indeed, the value of the leaves is known – since the leaves are ...
... formula is evaluated to true if and only if the root node of the formula is evaluated to true. In order to determine the value of this node given by an interpretation, one may compute the value of each node in reverse topological order; indeed, the value of the leaves is known – since the leaves are ...
One-dimensional Fragment of First-order Logic
... decidability questions have been studied. The fragment has recently been significantly generalized in [2]. The article introduces the guarded negation first-order logic GNFO. This logic only allows negations of formulae that are guarded in the sense of the guarded fragment. The guarded negation frag ...
... decidability questions have been studied. The fragment has recently been significantly generalized in [2]. The article introduces the guarded negation first-order logic GNFO. This logic only allows negations of formulae that are guarded in the sense of the guarded fragment. The guarded negation frag ...
An Introduction to Mathematical Logic
... In future we will use the following conventions for “metavariables”: “P ”,“Q”,“R” (with or without indices) denote predicates. “f ”,“g”,“h” (with or without indices) denote function signs. “c” (with or without indices) denote constants. “x”,“y”,“z” (with or without indices) denote variables. Remark ...
... In future we will use the following conventions for “metavariables”: “P ”,“Q”,“R” (with or without indices) denote predicates. “f ”,“g”,“h” (with or without indices) denote function signs. “c” (with or without indices) denote constants. “x”,“y”,“z” (with or without indices) denote variables. Remark ...
A Proof Theory for Generic Judgments
... that the sequent Γ0 , ∀xB −→ C is proved using the introduction of ∀ on the left from the premise Γ0 , B[t/x] −→ C, where t is some term. To reduce the rank of the cut formula ∀x.B between the sequents Γ −→ ∀x.B and Γ0 , ∀xB −→ C, the eigenvariable c in the sequent calculus proof Π(c) must be substi ...
... that the sequent Γ0 , ∀xB −→ C is proved using the introduction of ∀ on the left from the premise Γ0 , B[t/x] −→ C, where t is some term. To reduce the rank of the cut formula ∀x.B between the sequents Γ −→ ∀x.B and Γ0 , ∀xB −→ C, the eigenvariable c in the sequent calculus proof Π(c) must be substi ...
CS389L: Automated Logical Reasoning Lecture 1
... iff I 6|= F iff I |= F1 and I |= F2 iff I |= F1 or I |= F2 iff, I 6|= F1 or I |= F2 iff, I |= F1 and I |= F2 or I 6|= F1 and I 6|= F2 ...
... iff I 6|= F iff I |= F1 and I |= F2 iff I |= F1 or I |= F2 iff, I 6|= F1 or I |= F2 iff, I |= F1 and I |= F2 or I 6|= F1 and I 6|= F2 ...
On the Expressive Power of QLTL⋆
... Remark 1 (Notation in Fig. 1). Let L1 and L2 be two nodes in Fig. 1. If L2 is reachable from L1 but not vice versa, then L1 < L2 , e.g. EQ(F ) < EQ(U ). If neither L2 is reachable from L1 nor L1 is reachable from L2 , then L1 ⊥ L2 , e.g. EQ(F ) ⊥ L(U ). If L1 and L2 are reachable from each other (na ...
... Remark 1 (Notation in Fig. 1). Let L1 and L2 be two nodes in Fig. 1. If L2 is reachable from L1 but not vice versa, then L1 < L2 , e.g. EQ(F ) < EQ(U ). If neither L2 is reachable from L1 nor L1 is reachable from L2 , then L1 ⊥ L2 , e.g. EQ(F ) ⊥ L(U ). If L1 and L2 are reachable from each other (na ...
The Logic of Provability
... no trouble arises from pretending it is. Indeed, it’s common to make this interpretation concrete and write f (x̄) to represent the unique y such that F (x̄, y) holds in PA. Thus, while PA lacks an actual term for functions like 2x , it can construct p-terms for them that agree on all values and beh ...
... no trouble arises from pretending it is. Indeed, it’s common to make this interpretation concrete and write f (x̄) to represent the unique y such that F (x̄, y) holds in PA. Thus, while PA lacks an actual term for functions like 2x , it can construct p-terms for them that agree on all values and beh ...
Simple multiplicative proof nets with units
... conclusion of a ⊥-link) works. Worse, this new jump is by no means natural (if A is B ⊗ C, the new jump can either be B or C), which is quite unpleasant. As far as we know, the only solution consists in declaring that jumps are not part of the proof-net, but rather some control structure. It is then ...
... conclusion of a ⊥-link) works. Worse, this new jump is by no means natural (if A is B ⊗ C, the new jump can either be B or C), which is quite unpleasant. As far as we know, the only solution consists in declaring that jumps are not part of the proof-net, but rather some control structure. It is then ...
From Syllogism to Common Sense Normal Modal Logic
... ‣ We sketch as an example the correspondence between the modal logic axiom that defines the logic K4 and the first-order axiom that characterises the class of transitive frames: ...
... ‣ We sketch as an example the correspondence between the modal logic axiom that defines the logic K4 and the first-order axiom that characterises the class of transitive frames: ...
Predicate logic definitions
... 3. An assignment of an n-place property to each n-place predicate except the two-place identity predicate =. 4. An assignment of a function, which maps each member of the UD to a member of the UD, to each function expression. Sentences of PL are defined to be true or false in a given interpretation ...
... 3. An assignment of an n-place property to each n-place predicate except the two-place identity predicate =. 4. An assignment of a function, which maps each member of the UD to a member of the UD, to each function expression. Sentences of PL are defined to be true or false in a given interpretation ...
Kripke completeness revisited
... of a relational semantics of modal logic to which we now turn. 1.2. Kripke semantics What is known as Kripke semantics, also known under the neutral term relational semantics, was presented by Saul Kripke in 1959 for the modal logic S5. It was modified later to accommodate also other modal logics an ...
... of a relational semantics of modal logic to which we now turn. 1.2. Kripke semantics What is known as Kripke semantics, also known under the neutral term relational semantics, was presented by Saul Kripke in 1959 for the modal logic S5. It was modified later to accommodate also other modal logics an ...
