1 Formal Languages
... rigorous in the sense that they are stiff (think of the term ‘rigor mortis’) . Related to the formal/informal distinction is the distinction between natural language and artificial language; formal languages are a species of artificial language. Leaving lexicography aside for the moment, 20th Centur ...
... rigorous in the sense that they are stiff (think of the term ‘rigor mortis’) . Related to the formal/informal distinction is the distinction between natural language and artificial language; formal languages are a species of artificial language. Leaving lexicography aside for the moment, 20th Centur ...
![overhead 12/proofs in predicate logic [ov]](http://s1.studyres.com/store/data/011612593_1-f0437b45ca3df4f633ddcc6197d427a6-300x300.png)
overhead 12/proofs in predicate logic [ov]
... universal statement WAS derived from universal statements, we require that this instance is derived within a "flagged subproof" and apply the following restrictions: R1 A letter being flagged must be new to the proof, that is, it may not appear, either in a formula or as a letter being flagged, prev ...
... universal statement WAS derived from universal statements, we require that this instance is derived within a "flagged subproof" and apply the following restrictions: R1 A letter being flagged must be new to the proof, that is, it may not appear, either in a formula or as a letter being flagged, prev ...
- Horn-Representation of a Concept Lattice,
... ∧-closure of RK . By Proposition 1, R̂K can be represented by the Horn formula FK consisting of its prime implicates. This formula is the Horn representation of the concept lattice we wanted to derive. Definition Horn representation: Let C1 , C2 , . . . , Ck be the prime implicates of R̂K . The form ...
... ∧-closure of RK . By Proposition 1, R̂K can be represented by the Horn formula FK consisting of its prime implicates. This formula is the Horn representation of the concept lattice we wanted to derive. Definition Horn representation: Let C1 , C2 , . . . , Ck be the prime implicates of R̂K . The form ...
Truth Tables and Deductive Reasoning
... An argument is deductively valid if and only if the truth of its premises guarantees the truth of its conclusion. or, equivalently, An argument is deductively valid if and only if there is no way for its premises to all be true and its conclusion to be simultaneously false. • Al-Ghazali raised worri ...
... An argument is deductively valid if and only if the truth of its premises guarantees the truth of its conclusion. or, equivalently, An argument is deductively valid if and only if there is no way for its premises to all be true and its conclusion to be simultaneously false. • Al-Ghazali raised worri ...
Proofs 1 What is a Proof?
... Let’s try some numerical experimentation to check this proposition: p(0) = 41 which is prime. p(1) = 43 which is prime. p(2) = 47 which is prime. p(3) = 53 which is prime. . . . p(20) = 461 which is prime. Hmmm, starts to look like a plausible claim. In fact we can keep checking through n = 39 and c ...
... Let’s try some numerical experimentation to check this proposition: p(0) = 41 which is prime. p(1) = 43 which is prime. p(2) = 47 which is prime. p(3) = 53 which is prime. . . . p(20) = 461 which is prime. Hmmm, starts to look like a plausible claim. In fact we can keep checking through n = 39 and c ...
Hoare Logic, Weakest Liberal Preconditions
... semantics. It would also be possible to prove the validity of the triple using Hoare logic rules, but that would need some auxiliary results. The proof is performed by induction on the structure of statement s. We detail the proof only for the case of the while loop; the other cases are straightforw ...
... semantics. It would also be possible to prove the validity of the triple using Hoare logic rules, but that would need some auxiliary results. The proof is performed by induction on the structure of statement s. We detail the proof only for the case of the while loop; the other cases are straightforw ...
Introducing Quantified Cuts in Logic with Equality
... The method [5] for propositional logic is shown to never increase the size of proofs more than polynomially. Another approach to the compression of firstorder proofs by introduction of definitions for abbreviating terms is [19]. There is a large body of work on the generation of non-analytic formulas ...
... The method [5] for propositional logic is shown to never increase the size of proofs more than polynomially. Another approach to the compression of firstorder proofs by introduction of definitions for abbreviating terms is [19]. There is a large body of work on the generation of non-analytic formulas ...
Chpt-3-Proof - WordPress.com
... – If it’s not prime, let p* be a prime dividing (R+1). But p* cannot be any of p_1, p_2, … p_r (remainder 1 after division); so, p* not among initial list and thus p* is larger than p_r. • This contradicts our assumption that there is a finite set of primes, and therefore such an assumption has to b ...
... – If it’s not prime, let p* be a prime dividing (R+1). But p* cannot be any of p_1, p_2, … p_r (remainder 1 after division); so, p* not among initial list and thus p* is larger than p_r. • This contradicts our assumption that there is a finite set of primes, and therefore such an assumption has to b ...
2.3 Weakest Preconditions
... 3. Repeat until every such subformula has been handled. • The above extends readily into quantifier-free formulae φ: domain(φ) is obtained similarly by considering its connectives ∧, ∨, ¬, . . . as operators ◦ which do not need such handling (since they are defined everywhere). • If domain(. . . ) i ...
... 3. Repeat until every such subformula has been handled. • The above extends readily into quantifier-free formulae φ: domain(φ) is obtained similarly by considering its connectives ∧, ∨, ¬, . . . as operators ◦ which do not need such handling (since they are defined everywhere). • If domain(. . . ) i ...
Formal deduction in propositional logic
... • It is significant however that any proposed formal proof can be checked mechanically to decide whether it is indeed a formal proof of this scheme. • This is done by checking 1) whether the rules of formal deduction are correctly applied, and 2) whether the last term of the formal proof is identica ...
... • It is significant however that any proposed formal proof can be checked mechanically to decide whether it is indeed a formal proof of this scheme. • This is done by checking 1) whether the rules of formal deduction are correctly applied, and 2) whether the last term of the formal proof is identica ...
An Abridged Report - Association for the Advancement of Artificial
... of sentences. Because of this, the derivation from only knowing (1) and (2) to knowing (3) must be carried out completely outside the logic, as in McDermott and Doyle’s logic or in Reiter’s (in their case with appropriate metalogical arguments about fixed points or extensions). In this paper, we pre ...
... of sentences. Because of this, the derivation from only knowing (1) and (2) to knowing (3) must be carried out completely outside the logic, as in McDermott and Doyle’s logic or in Reiter’s (in their case with appropriate metalogical arguments about fixed points or extensions). In this paper, we pre ...
ML is not finitely axiomatizable over Cheq
... Cheq. If this were the case, it would imply that Cheq is not finitely axiomatizable. In this note we give a negative solution to Litak’s question by proving that ML is not finitely axiomatizable over Cheq. Thus, the connection between the Medvedev logic and Cheq is not as strong as it first appeared ...
... Cheq. If this were the case, it would imply that Cheq is not finitely axiomatizable. In this note we give a negative solution to Litak’s question by proving that ML is not finitely axiomatizable over Cheq. Thus, the connection between the Medvedev logic and Cheq is not as strong as it first appeared ...