Unification in Propositional Logic
... The explicit computation of mgus or of complete sets of unifiers seems to be less important (see the application to admissible rules) and, in any case, it is only a question of writing down explicitly defined substitutions (namely the θP ’s for P ∈ ΠA). ...
... The explicit computation of mgus or of complete sets of unifiers seems to be less important (see the application to admissible rules) and, in any case, it is only a question of writing down explicitly defined substitutions (namely the θP ’s for P ∈ ΠA). ...
Propositional Dynamic Logic of Regular Programs*+
... provided for both the programs and for the formulas that talk about programs. The program semantics is derived from the relational semantics of programs (cf. Hoare and Lauer [ll]) and the formula semantics is adopted from the relational semantics for modal logic introduced by Kripke [14]. Informally ...
... provided for both the programs and for the formulas that talk about programs. The program semantics is derived from the relational semantics of programs (cf. Hoare and Lauer [ll]) and the formula semantics is adopted from the relational semantics for modal logic introduced by Kripke [14]. Informally ...
Chapter 2. The Mathematical Structure of CTL
... where Γ is a structured configuration of formulas or structural term and A is a logical formula. The set STRUCT of structural terms needed for a sequent presentation of NL is very simple. STRUCT ::= FORM | (STRUCT ◦ STRUCT). The logical rules of the Gentzen system for NL are given in Figure 2.1. In ...
... where Γ is a structured configuration of formulas or structural term and A is a logical formula. The set STRUCT of structural terms needed for a sequent presentation of NL is very simple. STRUCT ::= FORM | (STRUCT ◦ STRUCT). The logical rules of the Gentzen system for NL are given in Figure 2.1. In ...
Introduction to logic
... features is reasoning. Reasoning can be viewed as the process of having a knowledge base (KB) and manipulating it to create new knowledge. Reasoning can be seen as comprised of 3 processes: 1. Perceiving stimuli from the environment; 2. Translating the stimuli in components of the KB; 3. Working on ...
... features is reasoning. Reasoning can be viewed as the process of having a knowledge base (KB) and manipulating it to create new knowledge. Reasoning can be seen as comprised of 3 processes: 1. Perceiving stimuli from the environment; 2. Translating the stimuli in components of the KB; 3. Working on ...
Bisimulation and public announcements in logics of
... modal logics have been used as a formal means of modeling the informal notion of knowledge. If the modal is K and ϕ is a formula, then the formula Kϕ is accordingly read, “ϕ is known.” While theories in this language can make various knowledge assertions such as Kϕ ⊃ Kψ, the language has no means of ...
... modal logics have been used as a formal means of modeling the informal notion of knowledge. If the modal is K and ϕ is a formula, then the formula Kϕ is accordingly read, “ϕ is known.” While theories in this language can make various knowledge assertions such as Kϕ ⊃ Kψ, the language has no means of ...
Interpolation for McCain
... here. According to Hintikka [1976; 1972], and Harrah [1975] a question can be regarded as denoting its set of possible answers (out of which an appropriate answer selects one). For example, in Harrah’s system our @P would be called the “assertive core” of the question, whereas his indicated replies ...
... here. According to Hintikka [1976; 1972], and Harrah [1975] a question can be regarded as denoting its set of possible answers (out of which an appropriate answer selects one). For example, in Harrah’s system our @P would be called the “assertive core” of the question, whereas his indicated replies ...
(formal) logic? - Departamento de Informática
... What is a (formal) logic? Logic is defined as the study of the principles of reasoning. One of its branches is symbolic logic, that studies formal logic. A formal logic is a language equipped with rules for deducing the truth of one sentence from that of another. A logic consists of ...
... What is a (formal) logic? Logic is defined as the study of the principles of reasoning. One of its branches is symbolic logic, that studies formal logic. A formal logic is a language equipped with rules for deducing the truth of one sentence from that of another. A logic consists of ...
Logical Consequence by Patricia Blanchette Basic Question (BQ
... Because of the expressive power of higher order logics, they can say things about a formal system S which are either true or false of that system, but which can not be derived using the deductive apparatus of that system. This is the basic insight captured in Gödel’s Incompleteness Theorem, but it i ...
... Because of the expressive power of higher order logics, they can say things about a formal system S which are either true or false of that system, but which can not be derived using the deductive apparatus of that system. This is the basic insight captured in Gödel’s Incompleteness Theorem, but it i ...
An Introduction to SOFL
... The use of parenthesis An expression is interpreted by applying the operator priority order unless parenthesis is used. For example: the expression not p and q or r <=> p => q and r is equivalent to the expression: (((not p) and q) or r) <=> (p => (q and r)) Parenthesis can be used to change the pr ...
... The use of parenthesis An expression is interpreted by applying the operator priority order unless parenthesis is used. For example: the expression not p and q or r <=> p => q and r is equivalent to the expression: (((not p) and q) or r) <=> (p => (q and r)) Parenthesis can be used to change the pr ...
Modal_Logics_Eyal_Ariel_151107
... logics, that we already know. •Every proposition p is a formula. • If A, B are formulas, then the following are also formulas: ...
... logics, that we already know. •Every proposition p is a formula. • If A, B are formulas, then the following are also formulas: ...
SCM Sweb
... – If we start from true assumptions and then apply these rules, the conclusions thus reached will also be true. – The rules preserve truth from the premises to the conclusions. – Truth is not lost if the rules are followed. ...
... – If we start from true assumptions and then apply these rules, the conclusions thus reached will also be true. – The rules preserve truth from the premises to the conclusions. – Truth is not lost if the rules are followed. ...
вдгжеиз © ¢ on every class of ordered finite struc
... on every class of ordered finite structures, that is to say, if is a class of ordered finite structures, then the class of polynomial-time computable queries on coincides with the class of queries definable in least fixedpoint logic on . Least fixed-point logic LFP is the extension of first- ...
... on every class of ordered finite structures, that is to say, if is a class of ordered finite structures, then the class of polynomial-time computable queries on coincides with the class of queries definable in least fixedpoint logic on . Least fixed-point logic LFP is the extension of first- ...
Modal Logic
... for basic modal logic is quite general (although it can be further generalized as we will see later) and can be refined to yield the properties appropriate for the intended application. We will concentrate on three different applications: logic of necessity, temporal logic and logic of knowledge. T ...
... for basic modal logic is quite general (although it can be further generalized as we will see later) and can be refined to yield the properties appropriate for the intended application. We will concentrate on three different applications: logic of necessity, temporal logic and logic of knowledge. T ...
Structural Multi-type Sequent Calculus for Inquisitive Logic
... the entailment relation of questions is a type of dependency relation considered in dependence logic. Inquisitive logic was axiomatized in [6], and this axiomatization is not closed under uniform substitution, which is a hurdle for a smooth proof-theoretic treatment for inquisitive logic. In [22], a ...
... the entailment relation of questions is a type of dependency relation considered in dependence logic. Inquisitive logic was axiomatized in [6], and this axiomatization is not closed under uniform substitution, which is a hurdle for a smooth proof-theoretic treatment for inquisitive logic. In [22], a ...
Comparing Constructive Arithmetical Theories Based - Math
... Recall that the theory CP V is the classical closure of IP V and P V1 is P V conservatively extended to first-order logic. It is known that, under the assumption CP V = P V1 , the polynomial hierarchy collapses, by a result of Krajicek, Pudlak and Takeuti (see [KPT]). Using the original construction ...
... Recall that the theory CP V is the classical closure of IP V and P V1 is P V conservatively extended to first-order logic. It is known that, under the assumption CP V = P V1 , the polynomial hierarchy collapses, by a result of Krajicek, Pudlak and Takeuti (see [KPT]). Using the original construction ...
Basic Logic and Fregean Set Theory - MSCS
... areas like computer algebra constructive logic may perform relatively more prominent functions. The idea of using models of nature with a logic different from the classical one is not new. Quantum logic has been used to model quantum mechanical phenomena. In this paper we restrict ourselves to const ...
... areas like computer algebra constructive logic may perform relatively more prominent functions. The idea of using models of nature with a logic different from the classical one is not new. Quantum logic has been used to model quantum mechanical phenomena. In this paper we restrict ourselves to const ...
Available on-line - Gert
... turn. We also know that the rules permit exactly one of twenty possible opening moves, any one of which leads to a position on the board describable by a sentence (e.g. “A white knight is at KR3 and all other pieces are in their initial positions”) expressing a proposition (in this case the proposit ...
... turn. We also know that the rules permit exactly one of twenty possible opening moves, any one of which leads to a position on the board describable by a sentence (e.g. “A white knight is at KR3 and all other pieces are in their initial positions”) expressing a proposition (in this case the proposit ...
Semantics of intuitionistic propositional logic
... Example 2.13 Here are some examples of distributive lattices. The first, second and fourth lattices on the top row are boolean algebras, while the other lattices are not. (Exercise: in each such case find the elements which lack complements.) ...
... Example 2.13 Here are some examples of distributive lattices. The first, second and fourth lattices on the top row are boolean algebras, while the other lattices are not. (Exercise: in each such case find the elements which lack complements.) ...
Localized Satisfiability For Multi-Context Systems
... our initial chain c0 should be most “general”, that is, all its components c0i must contain the entire set of local models Mi . Notice that c0 doesn’t satisfy any formula – in particular, c0 does not satisfy any bridge rule premise, and therefore complies with BR. The second implication of always ex ...
... our initial chain c0 should be most “general”, that is, all its components c0i must contain the entire set of local models Mi . Notice that c0 doesn’t satisfy any formula – in particular, c0 does not satisfy any bridge rule premise, and therefore complies with BR. The second implication of always ex ...
A MODAL EXTENSION OF FIRST ORDER CLASSICAL LOGIC–Part
... To this end we devise a particular modal extension of classical first order logic that simulates generalization in a natural manner and prove that it meets our main conservation requirement: For any classical formulae A and B and classical theory T , we have that T ∪ {A} proves B classically iff T p ...
... To this end we devise a particular modal extension of classical first order logic that simulates generalization in a natural manner and prove that it meets our main conservation requirement: For any classical formulae A and B and classical theory T , we have that T ∪ {A} proves B classically iff T p ...
Eliminating past operators in Metric Temporal Logic
... pointwise and continuous semantics) as the base logic to which distance operators are added. We show that for any formula in this base logic extended with the S modality, we can “eliminate” S subformulas from this formula in the sense that we can transform it to a formula over an extended set of pro ...
... pointwise and continuous semantics) as the base logic to which distance operators are added. We show that for any formula in this base logic extended with the S modality, we can “eliminate” S subformulas from this formula in the sense that we can transform it to a formula over an extended set of pro ...
MMConceptualComputationalRemainder
... conceptual proof (this happened to me): "Why, in a totally ordered set that statement is nothing but the contrapositive of transitivity!" Although this statement is merely a summary of the symbolic proof, it is enough to enable anyone conversant with simple logic to generate the symbolic proof. Furt ...
... conceptual proof (this happened to me): "Why, in a totally ordered set that statement is nothing but the contrapositive of transitivity!" Although this statement is merely a summary of the symbolic proof, it is enough to enable anyone conversant with simple logic to generate the symbolic proof. Furt ...
Using fuzzy temporal logic for monitoring behavior
... is a real value between 0 and 1. For example, the truth value of the proposition V isibleBall will be a real number between 0 and 1 reflecting our incapacity to draw clear boundaries between thruthness and falseness of a proposition. This allows us to include fuzzy statements such as “slightly visib ...
... is a real value between 0 and 1. For example, the truth value of the proposition V isibleBall will be a real number between 0 and 1 reflecting our incapacity to draw clear boundaries between thruthness and falseness of a proposition. This allows us to include fuzzy statements such as “slightly visib ...
Predicate Calculus - National Taiwan University
... How can we check if a formula is a tautology? If the domain is finite, then we can try all the possible interpretations (all the possible functions and predicates). But if the domain is infinite? Intuitively, this is why a computer cannot be programmed to determine if an arbitrary formula in predica ...
... How can we check if a formula is a tautology? If the domain is finite, then we can try all the possible interpretations (all the possible functions and predicates). But if the domain is infinite? Intuitively, this is why a computer cannot be programmed to determine if an arbitrary formula in predica ...