A MODAL EXTENSION OF FIRST ORDER CLASSICAL LOGIC–Part
... It is immediate by the conservation requirement that, conversely, a connected modal chain of type (3) can be replaced by a classical, possibly disconnected, chain of type (2). Modal extensions of propositional ([2], [8], [9], [10], [12], [17]) and predicate ([1], [3], [5], [9], [10], [11]) classical ...
... It is immediate by the conservation requirement that, conversely, a connected modal chain of type (3) can be replaced by a classical, possibly disconnected, chain of type (2). Modal extensions of propositional ([2], [8], [9], [10], [12], [17]) and predicate ([1], [3], [5], [9], [10], [11]) classical ...
Semi-constr. theories - Stanford Mathematics
... indefinite totality. Thus quantification over the natural numbers is taken to be definite, but not quantification applied to variables for sets or functions of natural numbers. Most axiomatizations of set theory that have been treated metamathematically have been based either entirely on classical ...
... indefinite totality. Thus quantification over the natural numbers is taken to be definite, but not quantification applied to variables for sets or functions of natural numbers. Most axiomatizations of set theory that have been treated metamathematically have been based either entirely on classical ...
Handout on Revenge
... I address question 1. in other work, in which ∆ is explicitly defined in terms of the notion of coherent rational preferences. However, we may still give something like an implicit definition of ∆ by outlining its role in a theory of rational propositional attitudes. For example, that one shouldn’t ...
... I address question 1. in other work, in which ∆ is explicitly defined in terms of the notion of coherent rational preferences. However, we may still give something like an implicit definition of ∆ by outlining its role in a theory of rational propositional attitudes. For example, that one shouldn’t ...
REDUCTIO AD ABSURDUM* (Proof by contradiction) Y.K. Leong
... recent vintage - if one may consider one hundred years ago as recent enough. The subject itself has only been recently introduced to elementary levels of education. We are referring to set theory. We are all aware of the controversy raised by the introduction of sets at the primary school level at t ...
... recent vintage - if one may consider one hundred years ago as recent enough. The subject itself has only been recently introduced to elementary levels of education. We are referring to set theory. We are all aware of the controversy raised by the introduction of sets at the primary school level at t ...
slides
... Want a way to prove partial correctness statements valid... ... without having to consider explicitly every store and interpretation! Idea: develop a proof system in which every theorem is a valid partial correctness statement Judgements of the form ⊢ {P} c {Q} De ned inductively using compositional ...
... Want a way to prove partial correctness statements valid... ... without having to consider explicitly every store and interpretation! Idea: develop a proof system in which every theorem is a valid partial correctness statement Judgements of the form ⊢ {P} c {Q} De ned inductively using compositional ...
Natural Deduction Proof System
... • Natural Deduction tries to follow the natural style of reasoning. Most of the proof consists of forward reasoning, i.e. deriving conclusions, deriving new conclusions from these conclusions, etc. Occasionally hypotheses are introduced or dropped. • A derivation is a tree where the nodes are the ru ...
... • Natural Deduction tries to follow the natural style of reasoning. Most of the proof consists of forward reasoning, i.e. deriving conclusions, deriving new conclusions from these conclusions, etc. Occasionally hypotheses are introduced or dropped. • A derivation is a tree where the nodes are the ru ...
PRESERVATION THEOREMS IN LUKASIEWICZ MODEL THEORY
... Below by T we mean a theory over Lukasiewicz predicate logic. A formula of the form ∀x̄φ where φ is quantifier-free is called universal. A theory is called universal if it is equivalent to a set of universal sentences. Following [10], we say an L-theory T has quantifier-elimination if every formula ...
... Below by T we mean a theory over Lukasiewicz predicate logic. A formula of the form ∀x̄φ where φ is quantifier-free is called universal. A theory is called universal if it is equivalent to a set of universal sentences. Following [10], we say an L-theory T has quantifier-elimination if every formula ...
Arithmetic as a theory modulo
... It should be noticed that second-order arithmetic can be embedded in simple type theory with the axiom of infinity and thus that it can be expressed in deduction modulo. Our presentation of first-order arithmetic in deduction modulo uses many ideas coming from second-order arithmetic. However, our p ...
... It should be noticed that second-order arithmetic can be embedded in simple type theory with the axiom of infinity and thus that it can be expressed in deduction modulo. Our presentation of first-order arithmetic in deduction modulo uses many ideas coming from second-order arithmetic. However, our p ...
The Compactness Theorem for first-order logic
... around each real number, and then some infinite “stuff” at both ends of the number line beyond all the standard numbers. Note though that there’s a lot of “layers” involved when doing this. For example, if δ is a nonstandard infinitesimal, and r is a standard real number, then rδ is a nonstandard in ...
... around each real number, and then some infinite “stuff” at both ends of the number line beyond all the standard numbers. Note though that there’s a lot of “layers” involved when doing this. For example, if δ is a nonstandard infinitesimal, and r is a standard real number, then rδ is a nonstandard in ...
Natural Deduction Calculus for Quantified Propositional Linear
... propositional linear-time temporal logic extended with propositional quantification [Sistla (1983)]. We follow the notation adopted in [French and Reynolds (2002)] calling this logic QPTL. Our construction naturally extends previously defined system for PLTL [Bolotov et al. (2006)] by new rules to c ...
... propositional linear-time temporal logic extended with propositional quantification [Sistla (1983)]. We follow the notation adopted in [French and Reynolds (2002)] calling this logic QPTL. Our construction naturally extends previously defined system for PLTL [Bolotov et al. (2006)] by new rules to c ...
PDF
... The diagonal lemma shows that in theories that can represent computability all formulas have a fixed point. Fixed point constructors, on the other hand, lead to inconsistencies, as they make it possible to define formulas that are equivalent to their own negation. Before we prove this, let us introd ...
... The diagonal lemma shows that in theories that can represent computability all formulas have a fixed point. Fixed point constructors, on the other hand, lead to inconsistencies, as they make it possible to define formulas that are equivalent to their own negation. Before we prove this, let us introd ...
Language of Logic 1-2B - Winterrowd-math
... The Mad Tea Party on p. 19 What was Alice’s false statement? What counterexamples to Alice’s logic were given by the Mad Hatter, the March Hare, and the Dormouse? What is the difference between “I mean what I say” and “I say what I mean”? If you had attended the tea party, what counterexample to Al ...
... The Mad Tea Party on p. 19 What was Alice’s false statement? What counterexamples to Alice’s logic were given by the Mad Hatter, the March Hare, and the Dormouse? What is the difference between “I mean what I say” and “I say what I mean”? If you had attended the tea party, what counterexample to Al ...
Knowledge Representation
... • There is a precise meaning to expressions in predicate logic. • Like in propositional logic, it is all about determining whether something is true or false. • X P(X) means that P(X) must be true for every object X in the domain of interest. • X P(X) means that P(X) must be true for at least on ...
... • There is a precise meaning to expressions in predicate logic. • Like in propositional logic, it is all about determining whether something is true or false. • X P(X) means that P(X) must be true for every object X in the domain of interest. • X P(X) means that P(X) must be true for at least on ...
