CS243, Logic and Computation Propositional Logic 1 Propositions
... 1. (Basis) The truth value of each basic proposition is as given directly by t. 2. (Recursion) If p and q are propositions over P with truth values t(p), t(q), then t(not p) = notf(t(p)), t(p and q) = andf(t(p),t(q)); t(p or q) = ort(t(p),t(q)), where opf in each case is the truth table for the oper ...
... 1. (Basis) The truth value of each basic proposition is as given directly by t. 2. (Recursion) If p and q are propositions over P with truth values t(p), t(q), then t(not p) = notf(t(p)), t(p and q) = andf(t(p),t(q)); t(p or q) = ort(t(p),t(q)), where opf in each case is the truth table for the oper ...
The Art of Ordinal Analysis
... a rough outline of the underlying ideas will be discussed next. The most common logical calculi are Hilbert-style systems. They are specified by delineating a collection of schematic logical axioms and some inference rules. The choice of axioms and rules is more or less arbitrary, only subject to th ...
... a rough outline of the underlying ideas will be discussed next. The most common logical calculi are Hilbert-style systems. They are specified by delineating a collection of schematic logical axioms and some inference rules. The choice of axioms and rules is more or less arbitrary, only subject to th ...
Simple multiplicative proof nets with units
... is the path composition of the previous GoI diagram. This provides a simple solution to the problems articulated by Girard above. Sliced-GoI composition for MALL nets. Section 7 continues the GoI theme, and shows how composition (turbo cut elimination) of MALL proof nets [HG03, HG05] can be viewed a ...
... is the path composition of the previous GoI diagram. This provides a simple solution to the problems articulated by Girard above. Sliced-GoI composition for MALL nets. Section 7 continues the GoI theme, and shows how composition (turbo cut elimination) of MALL proof nets [HG03, HG05] can be viewed a ...
Bounded Functional Interpretation
... on the decidability of prime formulas, not even for the verification of the interpretation (as m.f.i. does). It also interprets new classical principles, conspicuously weak König’s lemma. This should be compared with m.f.i.’s treatment of weak König’s lemma, according to which the lemma is elimina ...
... on the decidability of prime formulas, not even for the verification of the interpretation (as m.f.i. does). It also interprets new classical principles, conspicuously weak König’s lemma. This should be compared with m.f.i.’s treatment of weak König’s lemma, according to which the lemma is elimina ...
Proofs in Propositional Logic
... interactively a proof that the conclusion logically follows from the ...
... interactively a proof that the conclusion logically follows from the ...
Classical Propositional Logic
... DPLL and the refined CDCL algorithm are the practically best methods for PL The resolution calculus (Robinson 1969) has been introduced as a basis for automated theorem proving in first-order logic. We will see it in detail in the first-order logic part of this lecture Refined versions are still the ...
... DPLL and the refined CDCL algorithm are the practically best methods for PL The resolution calculus (Robinson 1969) has been introduced as a basis for automated theorem proving in first-order logic. We will see it in detail in the first-order logic part of this lecture Refined versions are still the ...
? A Unified Semantic Framework for Fully
... Various sequent calculi that seem to have completely different natures belong to the family of basic systems. For example, this includes standard sequent calculi for modal logics, as well as the usual multiple-conclusion systems for intuitionistic logic, its dual, and bi-intuitionistic logic. On the ...
... Various sequent calculi that seem to have completely different natures belong to the family of basic systems. For example, this includes standard sequent calculi for modal logics, as well as the usual multiple-conclusion systems for intuitionistic logic, its dual, and bi-intuitionistic logic. On the ...
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 ...
Logic - United States Naval Academy
... Exclusive or 1. Mathematical Symbol: , XOR 2. p q is true if either p is true or q is true, but not both. 3. The definition of exclusive or is displayed in a truth table p ...
... Exclusive or 1. Mathematical Symbol: , XOR 2. p q is true if either p is true or q is true, but not both. 3. The definition of exclusive or is displayed in a truth table p ...
A Calculus for Type Predicates and Type Coercion
... − A. Some of the rules of our calculus can introduce finite intersections of types, but there will still always be only finitely many types in a tableau. In particular, is a Noetherian ordering on T . Therefore, we can state the following definition: Definition 5. We call a tableau branch H type-satur ...
... − A. Some of the rules of our calculus can introduce finite intersections of types, but there will still always be only finitely many types in a tableau. In particular, is a Noetherian ordering on T . Therefore, we can state the following definition: Definition 5. We call a tableau branch H type-satur ...
INTERPLAYS OF KNOWLEDGE AND NON
... is an inference rule of the system. There are many interpretations of these axioms in the literature. As it is known, they reflect logical omniscience (D), axiom of knowledge (E) and forms of introspection (F) and (G). So we have two logics and there are two non-interdefinable operators: knowledge ...
... is an inference rule of the system. There are many interpretations of these axioms in the literature. As it is known, they reflect logical omniscience (D), axiom of knowledge (E) and forms of introspection (F) and (G). So we have two logics and there are two non-interdefinable operators: knowledge ...
Chapter 6: The Deductive Characterization of Logic
... show-lines, boxing, cancelling, etc. On the other hand, simple derivations, which form the backbone of all derivations, are not so complicated. A simple derivation does not involve show-lines or provisional assumptions. You start with the premises and apply inference rules (repeatedly, as necessary) ...
... show-lines, boxing, cancelling, etc. On the other hand, simple derivations, which form the backbone of all derivations, are not so complicated. A simple derivation does not involve show-lines or provisional assumptions. You start with the premises and apply inference rules (repeatedly, as necessary) ...