Normal modal logics (Syntactic characterisations)
... In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Whi ...
... In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ simply when A ∈ Σ. Whi ...
Topological Completeness of First-Order Modal Logic
... a completeness proof for first-order S4 modal logic with respect to topologicalsheaf semantics of Awodey-Kishida [3], which combines the possible-world formulation of sheaf semantics with the topos-theoretic interpretation of the 2 operator and of other symbols. Hence the logic we consider has the f ...
... a completeness proof for first-order S4 modal logic with respect to topologicalsheaf semantics of Awodey-Kishida [3], which combines the possible-world formulation of sheaf semantics with the topos-theoretic interpretation of the 2 operator and of other symbols. Hence the logic we consider has the f ...
Semantics of PL
... 1. Universe. To interpret and we need to know what these quantifiers range over. In formal semantics, interpret the universe as a non-empty set of objects. So it has to contain at least one thing, but there is no upper limit on the number or type of things it contains. Our book has ‘finite inter ...
... 1. Universe. To interpret and we need to know what these quantifiers range over. In formal semantics, interpret the universe as a non-empty set of objects. So it has to contain at least one thing, but there is no upper limit on the number or type of things it contains. Our book has ‘finite inter ...
Elementary Logic
... what we said above about the converse, it IS true that a statement and its contrapositive are equivalent. One way to see this is to notice that A ⇒ B is false only if A is true and B is false (see above), and the contrapositive (Not B) ⇒ (Not A) is false only if (Not B) is true and (Not A) is false ...
... what we said above about the converse, it IS true that a statement and its contrapositive are equivalent. One way to see this is to notice that A ⇒ B is false only if A is true and B is false (see above), and the contrapositive (Not B) ⇒ (Not A) is false only if (Not B) is true and (Not A) is false ...
Logic seminar
... Propositional logic • If there are n distinct atoms in a formula, then there will be 2n distinct interpretations for the formula. • Sometimes, if A1, ..., An are all atoms occurring in a formula, it may be more convenient to represent an interpretation by a set {m1, ..., mn}, where mi is either Ai ...
... Propositional logic • If there are n distinct atoms in a formula, then there will be 2n distinct interpretations for the formula. • Sometimes, if A1, ..., An are all atoms occurring in a formula, it may be more convenient to represent an interpretation by a set {m1, ..., mn}, where mi is either Ai ...
INTERPLAYS OF KNOWLEDGE AND NON
... instead of (C). The reader should also check [8] for a detailed research on noncontingency logics. ...
... instead of (C). The reader should also check [8] for a detailed research on noncontingency logics. ...
proceedings version
... A here-and-there model (HT model) is made up of two sets of propositional variables H (‘here’) and T (‘there’) such that H ⊆ T . The logical language to talk about such models has connectives ⊥, ∧, ∨, and ⇒. The latter is interpreted in a non-classical way and is therefore different from the materia ...
... A here-and-there model (HT model) is made up of two sets of propositional variables H (‘here’) and T (‘there’) such that H ⊆ T . The logical language to talk about such models has connectives ⊥, ∧, ∨, and ⇒. The latter is interpreted in a non-classical way and is therefore different from the materia ...
Computing Default Extensions by Reductions on OR
... disjunction of modalized propositional formulae of the form Oϕk . The O R-formula in the example reduces to Op ∨ Oq. The third step is to determine the set of extensions of the default theory from the simpler formula obtained in the second step. This task is trivial, since each disjunct has a unique ...
... disjunction of modalized propositional formulae of the form Oϕk . The O R-formula in the example reduces to Op ∨ Oq. The third step is to determine the set of extensions of the default theory from the simpler formula obtained in the second step. This task is trivial, since each disjunct has a unique ...
On Perfect Introspection with Quantifying-in
... replaced by ti. For the semantics, we need to specify when an atomic sentence is true and when a sentence is believed. The t r u t h of an arbitrary sentence is then defined by the usual recursive rules. While the t r u t h of atomic sentences is determined by worlds, belief is modeled in possiblewo ...
... replaced by ti. For the semantics, we need to specify when an atomic sentence is true and when a sentence is believed. The t r u t h of an arbitrary sentence is then defined by the usual recursive rules. While the t r u t h of atomic sentences is determined by worlds, belief is modeled in possiblewo ...
Chapter 1 Elementary Number Theory
... This is false and can be shown by solving the equation x2 = 25 Implication statements are often called “if…then..” statements but the notation for this is to use the implication symbol “”. Example 1 becomes x 5 2 x 10 Example 2 becomes x 2 25 x 5 ...
... This is false and can be shown by solving the equation x2 = 25 Implication statements are often called “if…then..” statements but the notation for this is to use the implication symbol “”. Example 1 becomes x 5 2 x 10 Example 2 becomes x 2 25 x 5 ...
POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a
... cal languages where oblique constructions are represented by intensional operators. The direct-discourse approaches are, however, threatened by (self-referential) paradoxes. Montague (1963) showed that the syntactic treatment of necessity as a predicate of sentences in the object language leads to i ...
... cal languages where oblique constructions are represented by intensional operators. The direct-discourse approaches are, however, threatened by (self-referential) paradoxes. Montague (1963) showed that the syntactic treatment of necessity as a predicate of sentences in the object language leads to i ...
A Mathematical Introduction to Modal Logic
... alethic modality. Furthermore, according to the modality of the given statement, we can analyze it from a modal logical perspective. If the sentence is uttered in the form ‘it is known to the agent that...” or “the agent knows that...”, then it is easy to see that epistemic modalities should be used ...
... alethic modality. Furthermore, according to the modality of the given statement, we can analyze it from a modal logical perspective. If the sentence is uttered in the form ‘it is known to the agent that...” or “the agent knows that...”, then it is easy to see that epistemic modalities should be used ...
Propositional Logic: Normal Forms
... assign true to all marked atoms, and false to the others. If φ is not true under ν, it means that there exists a conjunct P1 ∧ . . . ∧ Pki → P 0 of φ that is false. By the semantics, this can only mean that P1 ∧ . . . ∧ Pki is true but P 0 is false. However, by the definition of ν, all Pi s are mark ...
... assign true to all marked atoms, and false to the others. If φ is not true under ν, it means that there exists a conjunct P1 ∧ . . . ∧ Pki → P 0 of φ that is false. By the semantics, this can only mean that P1 ∧ . . . ∧ Pki is true but P 0 is false. However, by the definition of ν, all Pi s are mark ...
Distributed Knowledge
... the Hintikka model as above is a bit misleading: the worlds v and u are in fact the same world. That means that the intersection of the worlds accessible for a from w with those accessible for b is not empty. In other words, in the Hintikka model that corresponds to our example, the distributed k ...
... the Hintikka model as above is a bit misleading: the worlds v and u are in fact the same world. That means that the intersection of the worlds accessible for a from w with those accessible for b is not empty. In other words, in the Hintikka model that corresponds to our example, the distributed k ...
The King of France is, in fact, bald
... Note that crucial to this reasoning is the claim that (3) is accepted as true; it is relied upon in the derivation of the contradiction. So this is a case of a sentence that is judged true even though its subject fails to refer. Is C.I. Lewis’s account of the interpretation of (3) convincing? Some m ...
... Note that crucial to this reasoning is the claim that (3) is accepted as true; it is relied upon in the derivation of the contradiction. So this is a case of a sentence that is judged true even though its subject fails to refer. Is C.I. Lewis’s account of the interpretation of (3) convincing? Some m ...
i Preface
... computable, otherwise our insights would, in the relevant sense, be the output of an algorithm (viz. the algorithm which specifies the dynamics of the physics of the brain). There are obviously lots of lacunae in this argument, and the foregoing sketch is only the barest skeleton of the complete def ...
... computable, otherwise our insights would, in the relevant sense, be the output of an algorithm (viz. the algorithm which specifies the dynamics of the physics of the brain). There are obviously lots of lacunae in this argument, and the foregoing sketch is only the barest skeleton of the complete def ...