Structural Multi-type Sequent Calculus for Inquisitive Logic
... the entailment relation of questions is a type of dependency relation considered in dependence logic. Inquisitive logic was axiomatized in [6], and this axiomatization is not closed under uniform substitution, which is a hurdle for a smooth proof-theoretic treatment for inquisitive logic. In [22], a ...
... the entailment relation of questions is a type of dependency relation considered in dependence logic. Inquisitive logic was axiomatized in [6], and this axiomatization is not closed under uniform substitution, which is a hurdle for a smooth proof-theoretic treatment for inquisitive logic. In [22], a ...
Model theory makes formulas large
... In the context of algorithms, complexity, and finite model theory, questions about the efficiency of the normal forms, which are usually neglected in classical model theory, are of fundamental importance. These are the questions we address. By efficiency we mean the size of the formulas in normal fo ...
... In the context of algorithms, complexity, and finite model theory, questions about the efficiency of the normal forms, which are usually neglected in classical model theory, are of fundamental importance. These are the questions we address. By efficiency we mean the size of the formulas in normal fo ...
10 Inference
... ples. There are many and a large variety because different principles are combined, or made more complicated, etc. We can use this principle to prove the existence of irrational numbers. A real number u is rational if there are integers m and n such that u = m n and irrational otherwise. The set of ...
... ples. There are many and a large variety because different principles are combined, or made more complicated, etc. We can use this principle to prove the existence of irrational numbers. A real number u is rational if there are integers m and n such that u = m n and irrational otherwise. The set of ...
Mathematical Statements and Their Proofs
... Let a and b be two even integers. Since they are even, they can be written in the forms a = 2x and b = 2y for some integers x and y, respectively. Then, a + b can be written in the form 2x + 2y, giving the following equation: a + b = 2x + 2y = 2(x + y) From this, we see that a + b is divisible by 2. ...
... Let a and b be two even integers. Since they are even, they can be written in the forms a = 2x and b = 2y for some integers x and y, respectively. Then, a + b can be written in the form 2x + 2y, giving the following equation: a + b = 2x + 2y = 2(x + y) From this, we see that a + b is divisible by 2. ...
Document
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
propositions and connectives propositions and connectives
... propositions names: p, q, r, …, p0, p1, p2, … a name for false : ...
... propositions names: p, q, r, …, p0, p1, p2, … a name for false : ...
Partial Correctness Specification
... It is used to describe the acceptable initial states, and intended final states of programs ...
... It is used to describe the acceptable initial states, and intended final states of programs ...
slides - National Taiwan University
... |= is about semantics, rather than syntax For Σ = ∅, we have ∅ |= τ , simply written |= τ . It says every truth assignment satisfies τ . In this case, τ is a tautology. ...
... |= is about semantics, rather than syntax For Σ = ∅, we have ∅ |= τ , simply written |= τ . It says every truth assignment satisfies τ . In this case, τ is a tautology. ...
Available on-line - Gert
... In 1967, Anderson [2] defined his system of relevant deontic logic as follows: take relevant system R, add a propositional constant V (“the violation” or “the bad thing”), and define O (“it is obligatory that”) by O A = ¬A → V , where → is relevant implication. This proposal naturally leads to the q ...
... In 1967, Anderson [2] defined his system of relevant deontic logic as follows: take relevant system R, add a propositional constant V (“the violation” or “the bad thing”), and define O (“it is obligatory that”) by O A = ¬A → V , where → is relevant implication. This proposal naturally leads to the q ...
1 Chapter III Set Theory as a Theory of First Order Predicate Logic
... Here is an appealing and apparently clear picture of the "universe of all sets": Suppose that a set A of "individuals" or "Urelements" is given. Then we can form sets from those individuals; these will be subsets of A. We can then form sets of which these subsets of A are in turn members;. In fact, ...
... Here is an appealing and apparently clear picture of the "universe of all sets": Suppose that a set A of "individuals" or "Urelements" is given. Then we can form sets from those individuals; these will be subsets of A. We can then form sets of which these subsets of A are in turn members;. In fact, ...
January 12
... (e.g., physical objects, living things, mental objects, etc.), but are true of everything. Frege calls a truth that can be proved in this way analytic, as opposed to synthetic. (Note that all analytic truths are a priori.) In order to prove that arithmetic is analytic, Frege must construct a proof o ...
... (e.g., physical objects, living things, mental objects, etc.), but are true of everything. Frege calls a truth that can be proved in this way analytic, as opposed to synthetic. (Note that all analytic truths are a priori.) In order to prove that arithmetic is analytic, Frege must construct a proof o ...
Notes on `the contemporary conception of logic`
... Now, all this is put in place in Mendelson (along with e.g. a proof of that every truth-function is generated by some statement-form involving at most the connectives ∼, ∧, and ∨) over the first 17 pages of Chapter 1, before we get any talk at all of wffs, axioms or theorems of a formal theory. In o ...
... Now, all this is put in place in Mendelson (along with e.g. a proof of that every truth-function is generated by some statement-form involving at most the connectives ∼, ∧, and ∨) over the first 17 pages of Chapter 1, before we get any talk at all of wffs, axioms or theorems of a formal theory. In o ...
Monadic Second Order Logic and Automata on Infinite Words
... words and uses the Büchi acceptance condition (defined below). A Büchi automaton A is a tuple hQ, A, q0 , ∆, F i, where Q is the finite set of states, A is the alphabet, q0 ∈ Q is the start state, ∆ ⊆ Q × A × Q is the transition relation, and F ⊆ Q is the set of accept states. A run of A on w is a ...
... words and uses the Büchi acceptance condition (defined below). A Büchi automaton A is a tuple hQ, A, q0 , ∆, F i, where Q is the finite set of states, A is the alphabet, q0 ∈ Q is the start state, ∆ ⊆ Q × A × Q is the transition relation, and F ⊆ Q is the set of accept states. A run of A on w is a ...
Propositional Dynamic Logic of Regular Programs*+
... The definition of n@(Q) depends only on @(Y) which has been already well defined previously. The new structure 9 is over @i and & , where A,, = CD;- CD,,is the set of Q-variables introduced in taking the closure of F. At this point it is helpful to explain the role of the Q-variables in the proof. F ...
... The definition of n@(Q) depends only on @(Y) which has been already well defined previously. The new structure 9 is over @i and & , where A,, = CD;- CD,,is the set of Q-variables introduced in taking the closure of F. At this point it is helpful to explain the role of the Q-variables in the proof. F ...
←→ ↓ ↓ ←→ ←→ ←→ ←→ −→ −→ → The diagonal lemma as
... Gödel’s diagonal lemma (expressing formally the ability of first-order arithmetic to ‘talk about itself’) plays a key role in the proof of three main limitative theorems of logic: ...
... Gödel’s diagonal lemma (expressing formally the ability of first-order arithmetic to ‘talk about itself’) plays a key role in the proof of three main limitative theorems of logic: ...
Unification in Propositional Logic
... that u |=p A. In the other points q, θaA tries to make the forcing ‘as close as possible’ to a: if a(x) = 0, then x 6∈ (θaA)∗(u)(q) and if a(x) = 1, then x ∈ (θaA)∗(u)(q), unless this is impossible because in some point p ≥ q, we have u |=p A and u 6|=p x (recall that forcing in such p’s is not chan ...
... that u |=p A. In the other points q, θaA tries to make the forcing ‘as close as possible’ to a: if a(x) = 0, then x 6∈ (θaA)∗(u)(q) and if a(x) = 1, then x ∈ (θaA)∗(u)(q), unless this is impossible because in some point p ≥ q, we have u |=p A and u 6|=p x (recall that forcing in such p’s is not chan ...