Finite-variable fragments of first
... tiling of size N is a function t : N2N → C such that: (i) for all i, j (1 ≤ i < f (n), 1 ≤ j ≤ f (n)), ht(i, j), t(i + 1, j)i ∈ H, (ii) for all i, j (1 ≤ i ≤ f (n), 1 ≤ j < f (n)), ht(i, j), t(i, j +1)i ∈ V . (Here + denotes addition modulo N .) Intuitively, the elements of C represent types of unit ...
... tiling of size N is a function t : N2N → C such that: (i) for all i, j (1 ≤ i < f (n), 1 ≤ j ≤ f (n)), ht(i, j), t(i + 1, j)i ∈ H, (ii) for all i, j (1 ≤ i ≤ f (n), 1 ≤ j < f (n)), ht(i, j), t(i, j +1)i ∈ V . (Here + denotes addition modulo N .) Intuitively, the elements of C represent types of unit ...
Least and greatest fixed points in Ludics, CSL 2015, Berlin.
... erally, it is hard to tell what such proofs compute, when two proofs compute the same function, etc. It requires to step back from the finite, syntactic proof system under consideration and to start considering its semantics; this is the topic of the present paper. As our domain of interpretation of ...
... erally, it is hard to tell what such proofs compute, when two proofs compute the same function, etc. It requires to step back from the finite, syntactic proof system under consideration and to start considering its semantics; this is the topic of the present paper. As our domain of interpretation of ...
Argumentative Approaches to Reasoning with Maximal Consistency
... and now p ⇒ p is not eliminated anymore. Still, p ⇒ p can be re-attacked by ¬p ⇒ ¬p, and so forth. As a consequence, we have that S |6 ∼ p and S |6 ∼ ¬p. Note 3 The present setting of dynamic derivations may be viewed as an improvement of a similar setting, introduced in (Arieli and Straßer 2014). T ...
... and now p ⇒ p is not eliminated anymore. Still, p ⇒ p can be re-attacked by ¬p ⇒ ¬p, and so forth. As a consequence, we have that S |6 ∼ p and S |6 ∼ ¬p. Note 3 The present setting of dynamic derivations may be viewed as an improvement of a similar setting, introduced in (Arieli and Straßer 2014). T ...
PDF
... Gurevich (1988) formalized the notion of a logic capturing PTIME and conjectured a negative answer to the above question. We saw above that in the presence of a linear order, FO + IFP captures PTIME. It can also be seen that this built-in order is necessary. On arbitrary nite structures, FO + IFP c ...
... Gurevich (1988) formalized the notion of a logic capturing PTIME and conjectured a negative answer to the above question. We saw above that in the presence of a linear order, FO + IFP captures PTIME. It can also be seen that this built-in order is necessary. On arbitrary nite structures, FO + IFP c ...
Supplement: Conditional statements and basic methods of proof
... If 10 < 5, then 15 < 10. Although it may bother you, this statement is true since the hypothesis is vacuous. (If this bothers you, think of a conditional statement as a promise: “If it rains tomorrow, then I’ll give you a dollar,” for example. If it fails to rain on the day, then I can’t break my p ...
... If 10 < 5, then 15 < 10. Although it may bother you, this statement is true since the hypothesis is vacuous. (If this bothers you, think of a conditional statement as a promise: “If it rains tomorrow, then I’ll give you a dollar,” for example. If it fails to rain on the day, then I can’t break my p ...
Interpreting and Applying Proof Theories for Modal Logic
... 4 Note that from now on the operator will not be taken as primitive but as defined in the following standard way: A = ¬¬A, not because it couldn’t be primitive, but for compactnesss of presentation. 5 In Belnap’s original work on Display Logic, the modal operators are treated with another family ...
... 4 Note that from now on the operator will not be taken as primitive but as defined in the following standard way: A = ¬¬A, not because it couldn’t be primitive, but for compactnesss of presentation. 5 In Belnap’s original work on Display Logic, the modal operators are treated with another family ...
full text - pdf - reports on mathematical logic
... with the vsp are well known: they include the logic of relevance R and their sublogics such as the logic of entailment E, the logic of ticket entailment T, not to mention weak relevant logics among which Brady’s logic DR and its sublogics are undoubtedly the more important (cf. [3], [4], [6]). Never ...
... with the vsp are well known: they include the logic of relevance R and their sublogics such as the logic of entailment E, the logic of ticket entailment T, not to mention weak relevant logics among which Brady’s logic DR and its sublogics are undoubtedly the more important (cf. [3], [4], [6]). Never ...
Discrete Mathematics - Lyle School of Engineering
... Then P(x) is called a predicate or propositional function with respect to the set D if for each value of x in D, P(x) is a statement; i.e., P(x) is true or false Moreover, D is called the domain (universe) of discourse and x is called the free variable © Discrete Mathematical Structures: Theory and ...
... Then P(x) is called a predicate or propositional function with respect to the set D if for each value of x in D, P(x) is a statement; i.e., P(x) is true or false Moreover, D is called the domain (universe) of discourse and x is called the free variable © Discrete Mathematical Structures: Theory and ...
ordinal logics and the characterization of informal concepts of proof
... that however complicated the logical structure of A may be, e.g. however many iterated implications it may contain, J.* will be an assertion of the form: a certain concretely specified formula is provable in some 2^. Also note that an assertion PV{(EJLO) [P^ is a proof predicate and P^( r A * 1 )]} ...
... that however complicated the logical structure of A may be, e.g. however many iterated implications it may contain, J.* will be an assertion of the form: a certain concretely specified formula is provable in some 2^. Also note that an assertion PV{(EJLO) [P^ is a proof predicate and P^( r A * 1 )]} ...
An Unsolvable Problem of Elementary Number Theory Alonzo
... The purpose of the present paper is to propose a definition of effective calculability which is thought to correspond satisfactorily to the somewhat vague intuitive notion in terms of which problems of this class are often stated, and to show, by means of an example, that not every problem of this c ...
... The purpose of the present paper is to propose a definition of effective calculability which is thought to correspond satisfactorily to the somewhat vague intuitive notion in terms of which problems of this class are often stated, and to show, by means of an example, that not every problem of this c ...
