Quantitative Temporal Logics: PSPACE and below - FB3
... ϕ, where J is obtained from I by replacing the upper interval bound n by 1. In the following, we reduce satisfiability of QTLb formulas to the satisfiability of QTL1 -formula, i.e., QTLformulas in which all upper interval bounds have value 1. As the coding of numbers is not an issue in the latter lo ...
... ϕ, where J is obtained from I by replacing the upper interval bound n by 1. In the following, we reduce satisfiability of QTLb formulas to the satisfiability of QTL1 -formula, i.e., QTLformulas in which all upper interval bounds have value 1. As the coding of numbers is not an issue in the latter lo ...
Binary Decision Diagrams for First Order Predicate Logic
... Proof: The transformation operators can be formulated as rewrite rules.l1 and l2 are ...
... Proof: The transformation operators can be formulated as rewrite rules.l1 and l2 are ...
Section I(c)
... (c) is not a proposition because it contains an unknown, x . Since we do not know the value of x therefore we cannot say whether x 5 2 is true or false. ‘Britney Spears looks beautiful’ is not a proposition because beauty is subjective. Note that a proposition can be false such as (b) 5+3=7 and ...
... (c) is not a proposition because it contains an unknown, x . Since we do not know the value of x therefore we cannot say whether x 5 2 is true or false. ‘Britney Spears looks beautiful’ is not a proposition because beauty is subjective. Note that a proposition can be false such as (b) 5+3=7 and ...
1 Deductive Reasoning and Logical Connectives
... • ¬(p ∧ q): The Yankees and the Red Sox did not both win last night. • ¬p ∨ ¬q: Either the Yankees or the Red Sox lost last night. • ¬p ∧ ¬q: The Yankees and the Red Sox both lost last night. Example 7 Write negations for each of the following statements: • John is 6 feet tall and he weighs at least ...
... • ¬(p ∧ q): The Yankees and the Red Sox did not both win last night. • ¬p ∨ ¬q: Either the Yankees or the Red Sox lost last night. • ¬p ∧ ¬q: The Yankees and the Red Sox both lost last night. Example 7 Write negations for each of the following statements: • John is 6 feet tall and he weighs at least ...
A SHORT PROOF FOR THE COMPLETENESS OF
... In order to keep this note as short as possible, here we do not deal with extensions of paramodulation which make it more efficient. In particular, we do not analyze how to eliminate the functionally reflexive axioms. We assume that the reader is familiar with the theory of resolution calculus. For ...
... In order to keep this note as short as possible, here we do not deal with extensions of paramodulation which make it more efficient. In particular, we do not analyze how to eliminate the functionally reflexive axioms. We assume that the reader is familiar with the theory of resolution calculus. For ...
A simple proof of Parsons` theorem
... M∗ |= ∀x∃y¬ϕ(x, y, c). In fact, for x = tj (c, d1 , . . . , dj−1 ) take y = dj and use the fact that ¬ϕ is a universal formula and, therefore, downward absolute between M and M∗ . We have restricted the statement of the theorem to single variables u, x and y in order to make the proof more readabl ...
... M∗ |= ∀x∃y¬ϕ(x, y, c). In fact, for x = tj (c, d1 , . . . , dj−1 ) take y = dj and use the fact that ¬ϕ is a universal formula and, therefore, downward absolute between M and M∗ . We have restricted the statement of the theorem to single variables u, x and y in order to make the proof more readabl ...
Logic for Computer Science. Lecture Notes
... Finally we have to state clearly what kind of opinions (sentences) can be formulated in the language we deal with and, moreover, which of those opinions are true (valid), and which are false (invalid). Now we can investigate the subject of reasoning via the validity of expressed opinions. Such an ab ...
... Finally we have to state clearly what kind of opinions (sentences) can be formulated in the language we deal with and, moreover, which of those opinions are true (valid), and which are false (invalid). Now we can investigate the subject of reasoning via the validity of expressed opinions. Such an ab ...
On the use of fuzzy stable models for inconsistent classical logic
... imposing conditions on the underlying residuated lattice: Theorem 3. Let L ≡ ([0, 1], ≤, ∗, ←, ¬) be a residuated lattice with negation. If ∗ and ¬ are continuous operators, then every finite normal program P defined over L has at least a stable model. Proof: The idea is to apply Brouwer’s fix-point ...
... imposing conditions on the underlying residuated lattice: Theorem 3. Let L ≡ ([0, 1], ≤, ∗, ←, ¬) be a residuated lattice with negation. If ∗ and ¬ are continuous operators, then every finite normal program P defined over L has at least a stable model. Proof: The idea is to apply Brouwer’s fix-point ...
Verification Conditions Are Code - Electronics and Computer Science
... Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from the associativity of function composition. Working directly with program semantics is a model-theoretic approach, howev ...
... Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from the associativity of function composition. Working directly with program semantics is a model-theoretic approach, howev ...
The Future of Post-Human Mathematical Logic
... The Dialectic Constraints Imposed by the Principles..................234 Table 5.29. The Semantics of Existential Dialectics......................................237 Table 5.30. The Pragmatics of Existential Dialectics.....................................238 Table 5.31. The Freedom/Unfreedom Dialect ...
... The Dialectic Constraints Imposed by the Principles..................234 Table 5.29. The Semantics of Existential Dialectics......................................237 Table 5.30. The Pragmatics of Existential Dialectics.....................................238 Table 5.31. The Freedom/Unfreedom Dialect ...
Document
... proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no maMer what proposi:ons are subs:tuted into its proposi:onal variables. • ...
... proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no maMer what proposi:ons are subs:tuted into its proposi:onal variables. • ...
Hierarchical Introspective Logics
... with definitions of ordinals. This is not the same as indexing the levels by ordinals. Two quite different definitions might easily define the same mathematical ordinal yet also it could be very difficult to determine the precise comparative relationship of two different definitions, each of them s ...
... with definitions of ordinals. This is not the same as indexing the levels by ordinals. Two quite different definitions might easily define the same mathematical ordinal yet also it could be very difficult to determine the precise comparative relationship of two different definitions, each of them s ...
From proof theory to theories theory
... theorems, and thus require a theory, has be given up and proofs have been studied for for their own sake. A typical example is linear logic [24]. The thesis we shall develop in this paper is that there is another possible way to go for proof theory: modify the notion of theory so that it can be prop ...
... theorems, and thus require a theory, has be given up and proofs have been studied for for their own sake. A typical example is linear logic [24]. The thesis we shall develop in this paper is that there is another possible way to go for proof theory: modify the notion of theory so that it can be prop ...
An Introduction to Löb`s Theorem in MIRI Research
... There’s a different algorithm which (at the cost of using lots of computation) avoids that fragility. We call this agent FairBot, and it operates as follows: • Both FairBot and its opponent X are functions of one argument, which take the opponent’s source code and output either C or D. • When FairBo ...
... There’s a different algorithm which (at the cost of using lots of computation) avoids that fragility. We call this agent FairBot, and it operates as follows: • Both FairBot and its opponent X are functions of one argument, which take the opponent’s source code and output either C or D. • When FairBo ...
Chapter 1
... (a) It is false today is Friday. Or, today is not Friday. (b) All of the chairs are not broken in this room. (c) It is false x is less than 2. Or, x is greater or equal to 2. (d) Seven is not an even number. Or, seven is an odd number. (e) At least one chair is not broken in the room. Conditional St ...
... (a) It is false today is Friday. Or, today is not Friday. (b) All of the chairs are not broken in this room. (c) It is false x is less than 2. Or, x is greater or equal to 2. (d) Seven is not an even number. Or, seven is an odd number. (e) At least one chair is not broken in the room. Conditional St ...
remarks on synthetic tableaux for classical propositional calculus
... kind of questions (see [7] and chapter IV of [6] for more details). Nevertheless, many of basic intuitions underlying STM are similar to some formal techniques known in the literature. We shall mention three such connections. L. Kalmar’s proof of the completness of CPC is based on the fact that a CP ...
... kind of questions (see [7] and chapter IV of [6] for more details). Nevertheless, many of basic intuitions underlying STM are similar to some formal techniques known in the literature. We shall mention three such connections. L. Kalmar’s proof of the completness of CPC is based on the fact that a CP ...
A Concurrent Logical Framework: The Propositional Fragment Kevin Watkins , Iliano Cervesato
... stated informally as follows: the structure of canonical forms should be typedirected. This leads to the inversion principles necessary to prove the adequacy of encodings. For example, we would like to know that every term of type nat is of the form z or s t where t : nat. It is easy to see that the ...
... stated informally as follows: the structure of canonical forms should be typedirected. This leads to the inversion principles necessary to prove the adequacy of encodings. For example, we would like to know that every term of type nat is of the form z or s t where t : nat. It is easy to see that the ...
Formalizing Basic First Order Model Theory
... The most complex syntactic definition is of substitution. We have chosen a ‘name-carrying’ formalization of syntax, rather than indexing bound variables using some scheme following de Bruijn [1]. The latter is usually preferred when formalizing logical syntax precisely because substitution is simple ...
... The most complex syntactic definition is of substitution. We have chosen a ‘name-carrying’ formalization of syntax, rather than indexing bound variables using some scheme following de Bruijn [1]. The latter is usually preferred when formalizing logical syntax precisely because substitution is simple ...
Reading 2 - UConn Logic Group
... the predicate “r realizes F ” is not decidable. Kleene himself denied any connection of his realizability with BHK interpretation. It is also worth mentioning that Kleene realizability is not adequate for Int, i.e., there are realizable propositional formulas not derivable in Int (cf. [33], p. 53). ...
... the predicate “r realizes F ” is not decidable. Kleene himself denied any connection of his realizability with BHK interpretation. It is also worth mentioning that Kleene realizability is not adequate for Int, i.e., there are realizable propositional formulas not derivable in Int (cf. [33], p. 53). ...
Algebraizing Hybrid Logic - Institute for Logic, Language and
... the nominals (denoted by i, j, ...) behave similar to ordinary proposition letters, expect that nominals are true uniquely at a world. In other words, a nominal names a state by being true there and nowhere else. An example of a formula involving nominals is 33i → ¬3i. The language obtained by addin ...
... the nominals (denoted by i, j, ...) behave similar to ordinary proposition letters, expect that nominals are true uniquely at a world. In other words, a nominal names a state by being true there and nowhere else. An example of a formula involving nominals is 33i → ¬3i. The language obtained by addin ...
A Proof Theory for Generic Judgments
... a term built from variables in both of these signatures. Similarly, in the rule for ∀R (and, dually, for ∃L), the quantifier appears in the scope of the global signature Σ and the local signature σ. This quantifier can be instantiated (reading the rule bottom-up) with an eigenvariable whose intended ...
... a term built from variables in both of these signatures. Similarly, in the rule for ∀R (and, dually, for ∃L), the quantifier appears in the scope of the global signature Σ and the local signature σ. This quantifier can be instantiated (reading the rule bottom-up) with an eigenvariable whose intended ...