Chapter 5: Section 5-1 Mathematical Logic
... Mathematical Logic D. S. Malik Creighton University, Omaha, NE ...
... Mathematical Logic D. S. Malik Creighton University, Omaha, NE ...
Answer Sets for Propositional Theories
... (i) Γ1 is strongly equivalent to Γ2 , (ii) Γ1 is equivalent to Γ2 in the logic of here-and-there, and (iii) for each set X of atoms, Γ1X is equivalent to Γ2X in classical logic. The equivalence between (i) and (ii) is a generalization of the main result of [Lifschitz et al., 2001], and it is an imme ...
... (i) Γ1 is strongly equivalent to Γ2 , (ii) Γ1 is equivalent to Γ2 in the logic of here-and-there, and (iii) for each set X of atoms, Γ1X is equivalent to Γ2X in classical logic. The equivalence between (i) and (ii) is a generalization of the main result of [Lifschitz et al., 2001], and it is an imme ...
A game semantics for proof search: Preliminary results - LIX
... The proviso † requires that t and s are unifiable and θ is their most general unifier (∆θ is the multiset resulting from applying θ to all formulas in ∆). The proviso ‡ requires that t and s are not unifiable. The free variables of a sequent are also called eigenvariables. Notice that the equality r ...
... The proviso † requires that t and s are unifiable and θ is their most general unifier (∆θ is the multiset resulting from applying θ to all formulas in ∆). The proviso ‡ requires that t and s are not unifiable. The free variables of a sequent are also called eigenvariables. Notice that the equality r ...
Nonmonotonic Logic II: Nonmonotonic Modal Theories
... Of course, I have not proven that this is a fixed point, or the only fixed point. (As I will show below, if we had based the system on $5, there would be other fixed points.) In general, it is undecidable whether a formula appears in any fixed point or all of them. A computer program using nonmonoto ...
... Of course, I have not proven that this is a fixed point, or the only fixed point. (As I will show below, if we had based the system on $5, there would be other fixed points.) In general, it is undecidable whether a formula appears in any fixed point or all of them. A computer program using nonmonoto ...
Sequent-Systems for Modal Logic
... A rule, axiom or axiom-schema is eliminablefrom a system S if the subsystem of S without this rule, axiom or axiom-schema has the same theorems as S. It can easily be shown that a rule R is admissible in a system S iff it is eliminable from the extension of S with R. Our aim now is to show that D is ...
... A rule, axiom or axiom-schema is eliminablefrom a system S if the subsystem of S without this rule, axiom or axiom-schema has the same theorems as S. It can easily be shown that a rule R is admissible in a system S iff it is eliminable from the extension of S with R. Our aim now is to show that D is ...
Sequent calculus for predicate logic
... smaller than d. Then π can be transformed into a derivation π 0 with the same endsequent as π and which has cut rank strictly less than d. Proof. The idea is to look at the structure of the cut formula. We know what to do when it is an atomic formula or its main connective is propositional, because ...
... smaller than d. Then π can be transformed into a derivation π 0 with the same endsequent as π and which has cut rank strictly less than d. Proof. The idea is to look at the structure of the cut formula. We know what to do when it is an atomic formula or its main connective is propositional, because ...
SITUATION SEMANTICS AND MACHINE TRANSLATION
... then this requirement should not be affected by translation. This type of information is external to the text and therefore would not appear in the representation of the content and so would not be affected by translation. T h e only major alteration required in the context of the text is that the r ...
... then this requirement should not be affected by translation. This type of information is external to the text and therefore would not appear in the representation of the content and so would not be affected by translation. T h e only major alteration required in the context of the text is that the r ...
Seventy-five problems for testing automatic
... sort whose solution is, of itself, of any mathematical or logical interest. Such ‘open problems’ are regularly published in the Newsletter of the Association for Automated Reasoning. Most (but not all) of my problems can be found in elementary logic textbooks - but they have been chosen either becau ...
... sort whose solution is, of itself, of any mathematical or logical interest. Such ‘open problems’ are regularly published in the Newsletter of the Association for Automated Reasoning. Most (but not all) of my problems can be found in elementary logic textbooks - but they have been chosen either becau ...
A brief introduction to Logic and its applications
... (Curry-Howard). This is not possible due to the undecidability : if we take P to mean “program p halts on input x”, the excluded middle would yield a decider for the halting problem, which cannot exist. ...
... (Curry-Howard). This is not possible due to the undecidability : if we take P to mean “program p halts on input x”, the excluded middle would yield a decider for the halting problem, which cannot exist. ...
Least and greatest fixed points in Ludics, CSL 2015, Berlin.
... The formal sum a(~xa ).pa is the A-indexed family {a(~xa ).pa }a∈A . P P We write K⊆A a(~xa ).pa to denote the design a(~xa ).qa where qa = pa if a ∈ K and P P a(~xa ).Ω. In a negative design a(~xa ).pa , qa = Ω otherwise. We denote by Ω− the design a(~xa ) binds the variables ~xa appearing in pa . ...
... The formal sum a(~xa ).pa is the A-indexed family {a(~xa ).pa }a∈A . P P We write K⊆A a(~xa ).pa to denote the design a(~xa ).qa where qa = pa if a ∈ K and P P a(~xa ).Ω. In a negative design a(~xa ).pa , qa = Ω otherwise. We denote by Ω− the design a(~xa ) binds the variables ~xa appearing in pa . ...
preference based on reasons
... et al., 2009). Of particular relevance is Liu (2008, chap. 3). This work introduces “priorities” (which function like reasons in the present setting) that are ordered by importance, and integrated into a formal language of preference and belief. Several ways of extracting preferences from priorities ...
... et al., 2009). Of particular relevance is Liu (2008, chap. 3). This work introduces “priorities” (which function like reasons in the present setting) that are ordered by importance, and integrated into a formal language of preference and belief. Several ways of extracting preferences from priorities ...
2. First Order Logic 2.1. Expressions. Definition 2.1. A language L
... We will sometimes distinguish a special binary relation symbol =. 0-ary function symbols are called constant symbols. We will always assume that both LF and LR are countable. First-order logic will involve expressions built from symbols of our language together with additional symbols: • Infinitely ...
... We will sometimes distinguish a special binary relation symbol =. 0-ary function symbols are called constant symbols. We will always assume that both LF and LR are countable. First-order logic will involve expressions built from symbols of our language together with additional symbols: • Infinitely ...
Formal Theories of Truth INTRODUCTION
... It seems Tarski admits here that Convention T is highly incomplete: a good theory of truth should not only yield the T-sentences, it should also yield the general principle of contradiction ‘For any sentence (without True ) either the sentence or its negation is true.’ Perhaps Tarski thought that de ...
... It seems Tarski admits here that Convention T is highly incomplete: a good theory of truth should not only yield the T-sentences, it should also yield the general principle of contradiction ‘For any sentence (without True ) either the sentence or its negation is true.’ Perhaps Tarski thought that de ...
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... completeness only says that it must be possible to prove every valid formula correct with the tableau method but it doesn’t require that any attempt will succeed. And the fact that we weren’t able to find a proof with a not so bright approach doesn’t mean that there is none at all. Fortunately, we c ...
... completeness only says that it must be possible to prove every valid formula correct with the tableau method but it doesn’t require that any attempt will succeed. And the fact that we weren’t able to find a proof with a not so bright approach doesn’t mean that there is none at all. Fortunately, we c ...
