A really temporal logic
... Abstract. We introduce a temporal logic for the specification of real-time systems. Our logic, binds a TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier variable to the time of the local temporal context. TPTL is both a natural language for specification and a su ...
... Abstract. We introduce a temporal logic for the specification of real-time systems. Our logic, binds a TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier variable to the time of the local temporal context. TPTL is both a natural language for specification and a su ...
Intuitionistic and Modal Logic
... • But study of intuitionistic proofs and formal systems very alive. Only by fully accepting intuitionistic methods does one get proofs that guarantees to exhibit objects that are proved to exist. One gets this way the constructive part of mathematics. • Less popular but fascinating are Brouwer’s cho ...
... • But study of intuitionistic proofs and formal systems very alive. Only by fully accepting intuitionistic methods does one get proofs that guarantees to exhibit objects that are proved to exist. One gets this way the constructive part of mathematics. • Less popular but fascinating are Brouwer’s cho ...
preference based on reasons
... furniture, cat, and fireplace as before. Home with no fire alarm is the actual situation, hence especially easy to envision. If u 1 measures safety, and p is “A will purchase a fire alarm” then p 1 ¬ p holds inasmuch as the alarm improves safety. (Since is also true in A’s situation, p 1 ¬ p is ...
... furniture, cat, and fireplace as before. Home with no fire alarm is the actual situation, hence especially easy to envision. If u 1 measures safety, and p is “A will purchase a fire alarm” then p 1 ¬ p holds inasmuch as the alarm improves safety. (Since is also true in A’s situation, p 1 ¬ p is ...
many-valued logics - University of Sydney
... (In the rule for the biconditional in the Lukasiewicz systems, the conditional is then this Lukasiewicz conditional, not the Kleene conditional.) The idea here is that if the consequent is at least as true as the antecedent, then the conditional is completely true, while if the antecedent is truer ...
... (In the rule for the biconditional in the Lukasiewicz systems, the conditional is then this Lukasiewicz conditional, not the Kleene conditional.) The idea here is that if the consequent is at least as true as the antecedent, then the conditional is completely true, while if the antecedent is truer ...
On the use of fuzzy stable models for inconsistent classical logic
... the undefinedness is due to the explicit contradiction in the rules of the program whereas, in the latter case, u represents the uncertainty in knowing whether p is false and q true or vice versa. In order to obtain a more expressive approach, one can consider the stable model semantics, which allow ...
... the undefinedness is due to the explicit contradiction in the rules of the program whereas, in the latter case, u represents the uncertainty in knowing whether p is false and q true or vice versa. In order to obtain a more expressive approach, one can consider the stable model semantics, which allow ...
John L. Pollock
... name). Initially, the empty set is apt to seem paradoxical. How can we have a collection without anything in it? But reflection shows that the empty set is not really so strange as it may first appear. For example, a mathematician might consider the set of all solutions to a particular equation, pro ...
... name). Initially, the empty set is apt to seem paradoxical. How can we have a collection without anything in it? But reflection shows that the empty set is not really so strange as it may first appear. For example, a mathematician might consider the set of all solutions to a particular equation, pro ...
A proof
... first step is the assumption that p is true; subsequent steps are constructed using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we ...
... first step is the assumption that p is true; subsequent steps are constructed using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we ...
What is a Closed-Form Number?
... But since W is not an elementary function [5], this is not an answer that would satisfy most high-school students. Similarly, if we allow various special functions-e.g., elliptic, hypergeometric, or theta functions-then we can explicitly express the r, in Question 2, or indeed the roots of any polyn ...
... But since W is not an elementary function [5], this is not an answer that would satisfy most high-school students. Similarly, if we allow various special functions-e.g., elliptic, hypergeometric, or theta functions-then we can explicitly express the r, in Question 2, or indeed the roots of any polyn ...
Carnap and Quine on the analytic-synthetic - Philsci
... theory, and therefore in the next section the analyticity of set-theoretical statements is discussed. Quine does not regard set theoretical statements as analytic. This rather remarkable position can be explained on the basis of Quine’s own work in set theory. Quine draws a sharp distinction between ...
... theory, and therefore in the next section the analyticity of set-theoretical statements is discussed. Quine does not regard set theoretical statements as analytic. This rather remarkable position can be explained on the basis of Quine’s own work in set theory. Quine draws a sharp distinction between ...
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... e.g., [2]). These PSMs are used in practical knowledge systems. To get a better understanding of the different PSMs work has been done on the formalization of PSMs, e.g. [4, 10, 11]. In this paper we describe another approach, in which we adapt semantic tableaux to formalize PSMs. We show that this ...
... e.g., [2]). These PSMs are used in practical knowledge systems. To get a better understanding of the different PSMs work has been done on the formalization of PSMs, e.g. [4, 10, 11]. In this paper we describe another approach, in which we adapt semantic tableaux to formalize PSMs. We show that this ...
Chapter 1: The Foundations: Logic and Proofs
... Tautology: A compound proposition that is always true. Contradiction: A compound proposition that is always false. Contingency: A compound proposition that is neither a tautology nor a contradiction. ...
... Tautology: A compound proposition that is always true. Contradiction: A compound proposition that is always false. Contingency: A compound proposition that is neither a tautology nor a contradiction. ...
Sets, Numbers, and Logic
... But N0 is defective: you can add and multiply without leaving the system, but not always subtract: to solve x + 5 = 3, the system must be expanded to Z = {. . . , −2, −1, 0, 1, 2, . . .} : the integers. This causes some problems: negative numbers are traumatic — they don’t count anything, which is w ...
... But N0 is defective: you can add and multiply without leaving the system, but not always subtract: to solve x + 5 = 3, the system must be expanded to Z = {. . . , −2, −1, 0, 1, 2, . . .} : the integers. This causes some problems: negative numbers are traumatic — they don’t count anything, which is w ...
On atomic AEC and quasi-minimality
... Atomic abstract elementary class have been researched in connection with the model theory of infinitary logic. In recent years, the results were summarized by J.T.Baldin [1]. In that book, categoricity problem of atomic AEC is discussed mainly. I tried some local argument around the problem. Apology ...
... Atomic abstract elementary class have been researched in connection with the model theory of infinitary logic. In recent years, the results were summarized by J.T.Baldin [1]. In that book, categoricity problem of atomic AEC is discussed mainly. I tried some local argument around the problem. Apology ...
PROVING THE CORRECTNESS OF REGULA DETERMINISTIC
... Considering the diversity in language, notation and rigor which one finds in the relevant literature we are forced into adlpting, besides a simple programming language, an equally simple language for describing the types of correctness considered anl-,$the proof methods themselves. We have chosen to ...
... Considering the diversity in language, notation and rigor which one finds in the relevant literature we are forced into adlpting, besides a simple programming language, an equally simple language for describing the types of correctness considered anl-,$the proof methods themselves. We have chosen to ...