The Complete Proof Theory of Hybrid Systems
... We take a logical perspective, with which we study the logical foundations of hybrid systems and obtain interesting proof-theoretical relationships in spite of undecidability. We have developed a logic and proof calculus for hybrid systems [Pla08, Pla10b] in which it becomes meaningful to investigat ...
... We take a logical perspective, with which we study the logical foundations of hybrid systems and obtain interesting proof-theoretical relationships in spite of undecidability. We have developed a logic and proof calculus for hybrid systems [Pla08, Pla10b] in which it becomes meaningful to investigat ...
The Complete Proof Theory of Hybrid Systems
... is provable2 [18, BFC p. 245] and we also call it B. Axiom V is for vacuous modalities and requires that no free variable of φ (written F V (φ)) is bound by α. The converse holds, but we do not need it. Rule G is Gödel’s necessitation rule for modal logic [18]. Note that, unlike rule G, axiom V cru ...
... is provable2 [18, BFC p. 245] and we also call it B. Axiom V is for vacuous modalities and requires that no free variable of φ (written F V (φ)) is bound by α. The converse holds, but we do not need it. Rule G is Gödel’s necessitation rule for modal logic [18]. Note that, unlike rule G, axiom V cru ...
On Equivalent Transformations of Infinitary Formulas under the
... To make this claim precise, consider first the result of grounding rule (11) under the assumption that the Herbrand universe C is finite. In accordance with standard practice in ASP, we treat variable X as global and Y as local. Then the result of grounding (11) is the set of ground rules q(a) ← 1{p ...
... To make this claim precise, consider first the result of grounding rule (11) under the assumption that the Herbrand universe C is finite. In accordance with standard practice in ASP, we treat variable X as global and Y as local. Then the result of grounding (11) is the set of ground rules q(a) ← 1{p ...
Robot Morality and Review of classical logic.
... Suppose your waiter tells you that you can have either rice pilaf or baked potato with your dinner. In such circumstances, he plainly does not mean either rice pilaf or baked potato or both. You have to choose. So this use of “or” doesn’t fit the definition of disjunction given above. ...
... Suppose your waiter tells you that you can have either rice pilaf or baked potato with your dinner. In such circumstances, he plainly does not mean either rice pilaf or baked potato or both. You have to choose. So this use of “or” doesn’t fit the definition of disjunction given above. ...
Lesson 2-7 Proving Segment Relationships
... properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof. ...
... properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof. ...
methods of proof
... the real numbers. Although the precise statement of such theorems needs to include a universal quantifier, the standard convention in mathematics is to omit it. For example, the statement “If x > y, where x and y are positive real numbers, then x2 > y2.” really means “For all positive real numbers x ...
... the real numbers. Although the precise statement of such theorems needs to include a universal quantifier, the standard convention in mathematics is to omit it. For example, the statement “If x > y, where x and y are positive real numbers, then x2 > y2.” really means “For all positive real numbers x ...
Proof Theory: From Arithmetic to Set Theory
... • The patterns of reasoning described by Stoic logic are the patterns of interconnection between propositions that are completely independent of what those propositions say. • The first known systematic study of logic which involved quantifiers, components such as “for all” and “some”, was carried o ...
... • The patterns of reasoning described by Stoic logic are the patterns of interconnection between propositions that are completely independent of what those propositions say. • The first known systematic study of logic which involved quantifiers, components such as “for all” and “some”, was carried o ...
Discrete Mathematics and Logic II. Formal Logic
... These theorems show that there is no complete, consistent formal system that correctly describes the natural numbers, and that no su ciently strong system describing the natural numbers can prove its own consistency. These theorems are widely regarded as showing that Hilbert's program to nd a compl ...
... These theorems show that there is no complete, consistent formal system that correctly describes the natural numbers, and that no su ciently strong system describing the natural numbers can prove its own consistency. These theorems are widely regarded as showing that Hilbert's program to nd a compl ...
1 Introduction 2 Formal logic
... These equivalences show that some operators can be defined in terms of others. For example, by the substitution theorem and the last equivalence above, wherever we write ϕ ∨ ψ we could just as well write ¬ϕ → ψ. In particular, the above equivalences show that every operator can be expressed in terms ...
... These equivalences show that some operators can be defined in terms of others. For example, by the substitution theorem and the last equivalence above, wherever we write ϕ ∨ ψ we could just as well write ¬ϕ → ψ. In particular, the above equivalences show that every operator can be expressed in terms ...
