The Liar Paradox: A Consistent and Semantically Closed Solution
... the challenges presented by the Liar Paradox. Any meaningful discussion of, or solution to, the Liar Paradox must draw a clear distinction between the paradoxical cases and the non-paradoxical cases, and any proposed solution must satisfactorily deal with all paradoxical cases without incorrectly a ...
... the challenges presented by the Liar Paradox. Any meaningful discussion of, or solution to, the Liar Paradox must draw a clear distinction between the paradoxical cases and the non-paradoxical cases, and any proposed solution must satisfactorily deal with all paradoxical cases without incorrectly a ...
Syllogistic Logic with Complements
... 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 ` S means that there is a proof tree T for over Γ whose root is labeled S. We attached names to th ...
... 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 ` S means that there is a proof tree T for over Γ whose root is labeled S. We attached names to th ...
A Nonstandard Approach to the. Logical Omniscience Problem
... where all the rules of standard logic hold. For example, a formula is valid exactly if it is true in all the standard worlds in every structure. The intuition here is that the nonstandard worlds serve only as epistemic alternatives; although an agent may be muddled and may consider a nonstandard wor ...
... where all the rules of standard logic hold. For example, a formula is valid exactly if it is true in all the standard worlds in every structure. The intuition here is that the nonstandard worlds serve only as epistemic alternatives; although an agent may be muddled and may consider a nonstandard wor ...
Insincerity - Andreas Stokke
... I take it to be clear that in cases like this the speaker is not making an assertion. She is not asserting the proposition expressed by the sentence she utters; i.e. in this case that it was a really fun dinner. As it is often put, although the speaker says something, she is not asserting what she s ...
... I take it to be clear that in cases like this the speaker is not making an assertion. She is not asserting the proposition expressed by the sentence she utters; i.e. in this case that it was a really fun dinner. As it is often put, although the speaker says something, she is not asserting what she s ...
Hybrid Interactive Theorem Proving using Nuprl and HOL?
... a member of the set to the term constant, and if all the formulas in the \axioms" and \de nitions" sections of the theory hold for these objects, then all the theorems are true. In general, the semantics of a theory is parameterized by interpretations of all ancestor theories. The old semantics of N ...
... a member of the set to the term constant, and if all the formulas in the \axioms" and \de nitions" sections of the theory hold for these objects, then all the theorems are true. In general, the semantics of a theory is parameterized by interpretations of all ancestor theories. The old semantics of N ...
Equivalence of the information structure with unawareness to the
... are axioms of the logic of awareness. In modal logic, all axioms of a model are theorems of the model by assumption. All tautologies of propositional logic are also axioms of the logic of awareness. Additional theorems can be derived from the axioms and previous theorems using rules of inference. Th ...
... are axioms of the logic of awareness. In modal logic, all axioms of a model are theorems of the model by assumption. All tautologies of propositional logic are also axioms of the logic of awareness. Additional theorems can be derived from the axioms and previous theorems using rules of inference. Th ...
Answer Sets for Propositional Theories
... a formula is positive if it is in the antecedent of an even number of implications. An occurrence is strictly positive if such number is 0. An occurrence of an atom in a formula is negated if it is in a subformula of the form F ⊃ ⊥. For instance, in a formula (p ⊃ ⊥) ⊃ q, the occurrences of p and q ...
... a formula is positive if it is in the antecedent of an even number of implications. An occurrence is strictly positive if such number is 0. An occurrence of an atom in a formula is negated if it is in a subformula of the form F ⊃ ⊥. For instance, in a formula (p ⊃ ⊥) ⊃ q, the occurrences of p and q ...
Constructive Mathematics in Theory and Programming Practice
... (RUSS), and classical (that is, traditional) mathematics (CLASS): every theorem proved in Bishop is also a theorem, with the same proof, in INT, RUSS, and CLASS. Although Bishop has been criticised for his lack of precision about the notion of algorithm, it is precisely that 'defect' that allows it ...
... (RUSS), and classical (that is, traditional) mathematics (CLASS): every theorem proved in Bishop is also a theorem, with the same proof, in INT, RUSS, and CLASS. Although Bishop has been criticised for his lack of precision about the notion of algorithm, it is precisely that 'defect' that allows it ...
self-reference in arithmetic i - Utrecht University Repository
... theorem or Tarski’s theorem on the undefinability of truth, in the sense that the former are more sensitive to the choice of the formula expressing provability. The proof of Löb’s theorem also relies only on the existence of a fixed point of a certain formula. Whether this fixed point also states so ...
... theorem or Tarski’s theorem on the undefinability of truth, in the sense that the former are more sensitive to the choice of the formula expressing provability. The proof of Löb’s theorem also relies only on the existence of a fixed point of a certain formula. Whether this fixed point also states so ...
A Yabloesque paradox in epistemic game theory
... for Yablo-like sentences with ω-inconsistency (Ketland 2005). Furthermore, Barrio showed that Yablo’s Paradox in first-order arithmetic has a model and not inconsistent, but it is ω-inconsistent (Barrio 2010). It is easy to see how. Since every finite set of Sn sentences is satisfiable, then, by com ...
... for Yablo-like sentences with ω-inconsistency (Ketland 2005). Furthermore, Barrio showed that Yablo’s Paradox in first-order arithmetic has a model and not inconsistent, but it is ω-inconsistent (Barrio 2010). It is easy to see how. Since every finite set of Sn sentences is satisfiable, then, by com ...
