Symbolic Logic II
... wffs. How would you answer this? One way to think of the validity of a wff is if it is a tautology — that is, when all the truth values of a truth table are T (or 1). But if you think about Kleene’s truth tables, you will see that whenever all of the atomic components of a compound formula have the ...
... wffs. How would you answer this? One way to think of the validity of a wff is if it is a tautology — that is, when all the truth values of a truth table are T (or 1). But if you think about Kleene’s truth tables, you will see that whenever all of the atomic components of a compound formula have the ...
Lesson 2
... transposition de Morgan: p (q r) but q is true the second disjunct cannot be true the first is true: p (consequence) Hence Charles does not have a high blood pressure ...
... transposition de Morgan: p (q r) but q is true the second disjunct cannot be true the first is true: p (consequence) Hence Charles does not have a high blood pressure ...
First-Order Predicate Logic (2) - Department of Computer Science
... • Note that F |= G or F |= ¬G, for every sentence G. Thus, we have complete information about the domain of discourse. There are many examples where X 6|= G and X 6|= ¬G. We have incomplete information. • F |= G means that G is true in the structure F . Checking whether this is the case for finite F ...
... • Note that F |= G or F |= ¬G, for every sentence G. Thus, we have complete information about the domain of discourse. There are many examples where X 6|= G and X 6|= ¬G. We have incomplete information. • F |= G means that G is true in the structure F . Checking whether this is the case for finite F ...
Aristotle`s work on logic.
... one of the premisses is the conclusion of o1 (M ). Since the premisses were negative, the conclusion of o1 (M ) is positive. Since the other premiss of M is untouched by o 1 , we have that o1 (M ) has at least one negative premiss and a positive conclusion. The rest of the proof ho2 , ..., on i may ...
... one of the premisses is the conclusion of o1 (M ). Since the premisses were negative, the conclusion of o1 (M ) is positive. Since the other premiss of M is untouched by o 1 , we have that o1 (M ) has at least one negative premiss and a positive conclusion. The rest of the proof ho2 , ..., on i may ...
Lecture 4 - Michael De
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
What is...Linear Logic? Introduction Jonathan Skowera
... A ∩ B, selects points which are in A and B. This could be viewed as combing the two “theorems” on the left hand side into a single theorem which continues to imply the theorem on the right hand side. The small size of the above logical step admittedly makes the above inference mathematically uninter ...
... A ∩ B, selects points which are in A and B. This could be viewed as combing the two “theorems” on the left hand side into a single theorem which continues to imply the theorem on the right hand side. The small size of the above logical step admittedly makes the above inference mathematically uninter ...
Knowledge representation 1
... based on formal logic This makes logic a "gold standard" Other knowledge representations can be evaluated according to whether they produce the same results as formal logic, on a particular reasoning task. If they produce a different result, there's something wrong with them. ...
... based on formal logic This makes logic a "gold standard" Other knowledge representations can be evaluated according to whether they produce the same results as formal logic, on a particular reasoning task. If they produce a different result, there's something wrong with them. ...
A Proof of Cut-Elimination Theorem for U Logic.
... Basic Propositional Logic, BPL, was invented by Albert Visser in 1981 [5]. He wanted to interpret implication as formal provability. To protect his system against the liar paradox, modus ponens is weakened. His axiomatization of BPL uses natural deduction[3, p. 8]. The first sequent calculus for BPL ...
... Basic Propositional Logic, BPL, was invented by Albert Visser in 1981 [5]. He wanted to interpret implication as formal provability. To protect his system against the liar paradox, modus ponens is weakened. His axiomatization of BPL uses natural deduction[3, p. 8]. The first sequent calculus for BPL ...
A MODAL EXTENSION OF FIRST ORDER CLASSICAL LOGIC–Part
... disjoint from the original. For example, A1 ...
... disjoint from the original. For example, A1 ...
A short article for the Encyclopedia of Artificial Intelligence: Second
... ample (Dowty, Wall, & Peters, 1981). Forcing the implementer to encode the theoretician’s meanings into first-order logic can place a great distance between theory and implementation and can detract from the clarity of such implementations. Using a higher-order version of logic programming (Nadathu ...
... ample (Dowty, Wall, & Peters, 1981). Forcing the implementer to encode the theoretician’s meanings into first-order logic can place a great distance between theory and implementation and can detract from the clarity of such implementations. Using a higher-order version of logic programming (Nadathu ...
INTRODUCTION TO LOGIC Lecture 6 Natural Deduction Proofs in
... (1) Something is an Albanian penny. (2) Every Albanian penny is a quindarka. So, (C) something is a quindarka. Informal Proof. Let Smith be an Albanian penny. By (2), Smith is a quindarka. So, something is a quindarka. So (C), follows from (1) and (2). ...
... (1) Something is an Albanian penny. (2) Every Albanian penny is a quindarka. So, (C) something is a quindarka. Informal Proof. Let Smith be an Albanian penny. By (2), Smith is a quindarka. So, something is a quindarka. So (C), follows from (1) and (2). ...
Three Meanings of Epistemic Rhetoric
... A second way in which “rhetoric is epistemic” is in a sociological sense. This meaning straddles the first and third meanings argued in this paper and is therefore somewhat more complicated and subtle. In this view, whether rhetoric properly leads to the discovery of all truth is problematic. This p ...
... A second way in which “rhetoric is epistemic” is in a sociological sense. This meaning straddles the first and third meanings argued in this paper and is therefore somewhat more complicated and subtle. In this view, whether rhetoric properly leads to the discovery of all truth is problematic. This p ...
Modal_Logics_Eyal_Ariel_151107
... holds” or in other terms “after every terminating execution of , holds”. ...
... holds” or in other terms “after every terminating execution of , holds”. ...
ARISTOTLE`S SYLLOGISM: LOGIC TAKES FORM
... Aristotle's syllogism is referred to as formal logic. In order to better understand the impact of Aristotle's logic, let us consider what formal logic means today. Lukaswicz states that "Modern formal logic strives to attain the greatest possible exactness. This aim can be reached only by means of a ...
... Aristotle's syllogism is referred to as formal logic. In order to better understand the impact of Aristotle's logic, let us consider what formal logic means today. Lukaswicz states that "Modern formal logic strives to attain the greatest possible exactness. This aim can be reached only by means of a ...
4. Propositional Logic Using truth tables
... The formula A* is the dual of A. It is obtained from A by switching conjunctions to disjunctions. 1. What is the dual of (p0∨¬p1)∧p2? 2. Show that if A is a tautology, so is ¬A*. 3. Show that if A and B are equivalent, then so ...
... The formula A* is the dual of A. It is obtained from A by switching conjunctions to disjunctions. 1. What is the dual of (p0∨¬p1)∧p2? 2. Show that if A is a tautology, so is ¬A*. 3. Show that if A and B are equivalent, then so ...
The Diagonal Lemma Fails in Aristotelian Logic
... the term (∃x)Fx as a presupposition. It means that ~(Ex)Fx does not imply that A is false, but rather (Ex)Fx “is a necessary precondition not merely of of the truth of what is said, but of its being either true or false.” [Original italics] (Strawson, p. 174) We will, however, do one better and take ...
... the term (∃x)Fx as a presupposition. It means that ~(Ex)Fx does not imply that A is false, but rather (Ex)Fx “is a necessary precondition not merely of of the truth of what is said, but of its being either true or false.” [Original italics] (Strawson, p. 174) We will, however, do one better and take ...
Lindenbaum lemma for infinitary logics
... Lindenbaum lemma says that for any finitary logic ` (i.e., a finitary substitution-invariant consequence relation over the set of formulas of a given language) each theory (i.e., a set of formulas closed under `) not containing a formula ϕ can be extended into a maximal theory not containing ϕ. The ...
... Lindenbaum lemma says that for any finitary logic ` (i.e., a finitary substitution-invariant consequence relation over the set of formulas of a given language) each theory (i.e., a set of formulas closed under `) not containing a formula ϕ can be extended into a maximal theory not containing ϕ. The ...
Assumption Sets for Extended Logic Programs
... where the Li and Kj are literals. The consequent K1 ∨ . . . ∨ Kk of a formula ϕ of form (1) is called the head and denoted by h(ϕ). The antecedent L1 ∧ . . . ∧ Lm ∧ ¬Lm+1 ∧ . . . ¬ ∧ Ln is called the body and denoted by b(ϕ). We distinguish between the weakly positive part of the body, denoted by b+ ...
... where the Li and Kj are literals. The consequent K1 ∨ . . . ∨ Kk of a formula ϕ of form (1) is called the head and denoted by h(ϕ). The antecedent L1 ∧ . . . ∧ Lm ∧ ¬Lm+1 ∧ . . . ¬ ∧ Ln is called the body and denoted by b(ϕ). We distinguish between the weakly positive part of the body, denoted by b+ ...
To What Type of Logic Does the "Tetralemma" Belong?
... Perhaps, as is commonly suggested, Nagarjuna was simply trying to express a mystical rejection of analytical thought itself. However, it seems worth pointing out that anhomomorphic logic opens up another interpretation, perhaps consistent with the mystical one, but not really requiring it. Namely o ...
... Perhaps, as is commonly suggested, Nagarjuna was simply trying to express a mystical rejection of analytical thought itself. However, it seems worth pointing out that anhomomorphic logic opens up another interpretation, perhaps consistent with the mystical one, but not really requiring it. Namely o ...
PDF
... of the following forms: B → C, ¬B, or ∀xB, where B, C are wff’s. If A were B → C or ¬B, by induction, since B and C were in Γ, A is in Γ as a result. If A were ∀xB, then A is quasi-atomic, and therefore in Γ by the definition of Γ. Unique readability follows from the unique readability of wff’s of p ...
... of the following forms: B → C, ¬B, or ∀xB, where B, C are wff’s. If A were B → C or ¬B, by induction, since B and C were in Γ, A is in Γ as a result. If A were ∀xB, then A is quasi-atomic, and therefore in Γ by the definition of Γ. Unique readability follows from the unique readability of wff’s of p ...
slides
... ... 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 and (mostly) syntax-directed axioms and inference rules ...
... ... 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 and (mostly) syntax-directed axioms and inference rules ...
IS IT EASY TO LEARN THE LOGIC
... Frequently one encounters questions like, what is the use of logical principles if they are not used operationally like the De Morgan’s Laws or Modus Ponens? What is the importance of learning them and mention them? In colloquial language, saying “Mary studies at the Catholic University imply that M ...
... Frequently one encounters questions like, what is the use of logical principles if they are not used operationally like the De Morgan’s Laws or Modus Ponens? What is the importance of learning them and mention them? In colloquial language, saying “Mary studies at the Catholic University imply that M ...
Logic: Introduction - Department of information engineering and
... • Semantics: To make sure that different implementation of a programming language yield the same results, programming languages need to have a formal semantics. Logic provide the tool to develop such a semantics. Contents ...
... • Semantics: To make sure that different implementation of a programming language yield the same results, programming languages need to have a formal semantics. Logic provide the tool to develop such a semantics. Contents ...
Logic, deontic. The study of principles of reasoning pertaining to
... Logic, deontic. The study of principles of reasoning pertaining to obligation, permission, prohibition, moral commitment and other normative matters. Although often described as a branch of logic, deontic logic lacks the "topic-neutrality" characteristic of logic proper. It is better viewed as an ap ...
... Logic, deontic. The study of principles of reasoning pertaining to obligation, permission, prohibition, moral commitment and other normative matters. Although often described as a branch of logic, deontic logic lacks the "topic-neutrality" characteristic of logic proper. It is better viewed as an ap ...