Introduction to Modal and Temporal Logic
... Motivation: Give an intuitive meaning to syntactic symbols. Motivation: Give the meaning of “ϕ is true” Motivation: Define a meaning of “ϕ is a logical consequence of Γ” ...
... Motivation: Give an intuitive meaning to syntactic symbols. Motivation: Give the meaning of “ϕ is true” Motivation: Define a meaning of “ϕ is a logical consequence of Γ” ...
A New Theory of Content
... A propositional variable ß is relevant to wff iff there is some model P of such that there is some interpretation P' which differs from P in and only in the value P' assigns to ß and P' is not a model of . An (full or partial) interpretation P' is an extension of partial interpretation P iff fo ...
... A propositional variable ß is relevant to wff iff there is some model P of such that there is some interpretation P' which differs from P in and only in the value P' assigns to ß and P' is not a model of . An (full or partial) interpretation P' is an extension of partial interpretation P iff fo ...
Equivalence for the G3'-stable models semantics
... which two programs are strongly G03 -equivalent also guarantee that two disjunctive programs are strongly equivalent in the p-stable semantics. We present two main results that guarantee G03 strong equivalence, one for two arbitrary programs and another one for a couple of programs of the form P , P ...
... which two programs are strongly G03 -equivalent also guarantee that two disjunctive programs are strongly equivalent in the p-stable semantics. We present two main results that guarantee G03 strong equivalence, one for two arbitrary programs and another one for a couple of programs of the form P , P ...
8.3 Conditional Statements and Material Implication
... and inserting the word “then” between them, the resulting compound statement is a conditional statement (also called a hypothetical, an implication, or an implicative statement). In a conditional statement the component statement that follows the “if” is called the antecedent (or the implicans or—ra ...
... and inserting the word “then” between them, the resulting compound statement is a conditional statement (also called a hypothetical, an implication, or an implicative statement). In a conditional statement the component statement that follows the “if” is called the antecedent (or the implicans or—ra ...
The Bene ts of Relaxing Punctuality1
... requirements of systems ought to be modeled, speci ed, and veri ed. Most of these approaches are situated at either extreme of the trade-o between realistic modeling of time and feasible veri cation of timing properties. Typically, they either use a continuous model of time at the expense of decida ...
... requirements of systems ought to be modeled, speci ed, and veri ed. Most of these approaches are situated at either extreme of the trade-o between realistic modeling of time and feasible veri cation of timing properties. Typically, they either use a continuous model of time at the expense of decida ...
Incompleteness in the finite domain
... should also hold true with suitable bounds on the lengths of proofs. The prime example is the Second Incompleteness Theorem discussed above. Second, some results in proof complexity and bounded arithmetic seem to follow a general pattern. For example, as we noted above, polynomial time computations ...
... should also hold true with suitable bounds on the lengths of proofs. The prime example is the Second Incompleteness Theorem discussed above. Second, some results in proof complexity and bounded arithmetic seem to follow a general pattern. For example, as we noted above, polynomial time computations ...
THE PARADOXES OF STRICT IMPLICATION John L
... implication with a relation between meanings. However, we must be more explicit about just what this relation is. Let us begin with the case of analytic equivalence. It is probably the predominant view that the statement that p (e.g., the statement that 2 + 2 = 4) and the statement that q are analyt ...
... implication with a relation between meanings. However, we must be more explicit about just what this relation is. Let us begin with the case of analytic equivalence. It is probably the predominant view that the statement that p (e.g., the statement that 2 + 2 = 4) and the statement that q are analyt ...
Modal fixpoint logic: some model theoretic questions
... of recursive principle. At the end of the 1970s, Amir Pnueli [Pnu77] argued that linear temporal logic (LTL), which is obtained by restricting to models based on the natural numbers and by adding the “until” operator to modal logic, could be a useful formalism in that respect. Since then, other temp ...
... of recursive principle. At the end of the 1970s, Amir Pnueli [Pnu77] argued that linear temporal logic (LTL), which is obtained by restricting to models based on the natural numbers and by adding the “until” operator to modal logic, could be a useful formalism in that respect. Since then, other temp ...
Incompleteness in the finite domain
... and bounded arithmetic seem to follow a general pattern. For example, as we noted above, polynomial time computations are associated with the theory S21 by a witnessing theorem. If we take S22 , which we believe is a stronger theory, then the corresponding function class is PNP ,2 which we believe i ...
... and bounded arithmetic seem to follow a general pattern. For example, as we noted above, polynomial time computations are associated with the theory S21 by a witnessing theorem. If we take S22 , which we believe is a stronger theory, then the corresponding function class is PNP ,2 which we believe i ...
Online preprint - Villanova Computer Science
... connective ¬ is thus an operation on games. But this is normal because propositions for us are nothing but games, and propositional connectives — operations on games. ...
... connective ¬ is thus an operation on games. But this is normal because propositions for us are nothing but games, and propositional connectives — operations on games. ...
Admissible Infinitary Rules in Modal Logic. Part II
... Any (Kripke) structure F = (V , R) consists of a non-empty set V and a binary relation R on V . Each F = (V , R) determines a modal algebra F+ , on the power set A = P(V ), with a = {x ∈ V : R(x) ⊆ a}, where R(x) = {y ∈ V : xRy }. A subset C of V is called a cluster if xRy and yRx, for each x, y ∈ ...
... Any (Kripke) structure F = (V , R) consists of a non-empty set V and a binary relation R on V . Each F = (V , R) determines a modal algebra F+ , on the power set A = P(V ), with a = {x ∈ V : R(x) ⊆ a}, where R(x) = {y ∈ V : xRy }. A subset C of V is called a cluster if xRy and yRx, for each x, y ∈ ...
