Document
... Q0, Q1, ... , Qn+1, ... are queries, each empty or with one atom selected in it; θ1, θ2, ... , θn+1, ... are substitutions; c1, c2, ... , cn+1, ... are clause of P; For every SLD-derivation step, standardisation apart holds. ...
... Q0, Q1, ... , Qn+1, ... are queries, each empty or with one atom selected in it; θ1, θ2, ... , θn+1, ... are substitutions; c1, c2, ... , cn+1, ... are clause of P; For every SLD-derivation step, standardisation apart holds. ...
On Provability Logic
... fact that nested modalities are rare in natural language. We seldom say that it is necessary that something is possible and thus there is no agreement whether for instance the modal propositional formula 3p → 23p should be accepted as a modal tautology. This paper is devoted to provability logic, wh ...
... fact that nested modalities are rare in natural language. We seldom say that it is necessary that something is possible and thus there is no agreement whether for instance the modal propositional formula 3p → 23p should be accepted as a modal tautology. This paper is devoted to provability logic, wh ...
Mathematische Logik - WS14/15 Iosif Petrakis, Felix Quirin Weitk¨ amper November 13, 2014
... (B) m = 0. The corresponding (∗)-condition is that φ ∈ S(L) i.e., φ is a sentence. The definitional clauses are: (G1) A |= t1 = t2 iff t1 A = t2 A . (G2) A |= Rt1 . . . tn iff RA (t1 A . . . tn A ). (G3) A |= ¬φ iff not A |= φ. (G4) A |= (φ ∨ ψ) iff A |= φ or A |= ψ. (G5s) A |= (∃x ψ) iff there exis ...
... (B) m = 0. The corresponding (∗)-condition is that φ ∈ S(L) i.e., φ is a sentence. The definitional clauses are: (G1) A |= t1 = t2 iff t1 A = t2 A . (G2) A |= Rt1 . . . tn iff RA (t1 A . . . tn A ). (G3) A |= ¬φ iff not A |= φ. (G4) A |= (φ ∨ ψ) iff A |= φ or A |= ψ. (G5s) A |= (∃x ψ) iff there exis ...
Chapter 2 - Princeton University Press
... have stated their definitions and theorems with enough precision and clarity that any competent mathematician reading the work could expand it to a complete formalization if so desired. Formalizability is a requirement for mathematical publications in refereed research journals; formalizability give ...
... have stated their definitions and theorems with enough precision and clarity that any competent mathematician reading the work could expand it to a complete formalization if so desired. Formalizability is a requirement for mathematical publications in refereed research journals; formalizability give ...
Algebraizing Hybrid Logic - Institute for Logic, Language and
... Remark 2.4.2. The systematic tableau construction is defined in [5]. Roughly speaking, this construction is needed in order to prove strong completeness. Theorem 2.4.1. ([5]) Any consistent set of formulas in countable language is satisfiable in a countable standard model. The following theorem is t ...
... Remark 2.4.2. The systematic tableau construction is defined in [5]. Roughly speaking, this construction is needed in order to prove strong completeness. Theorem 2.4.1. ([5]) Any consistent set of formulas in countable language is satisfiable in a countable standard model. The following theorem is t ...
Appendix B
... Expression (let ((a 5) (b 8)) (+ a b)) is an abbreviation of the function application ((lambda (a b) (+ a b)) 5 8); Both expressions return the value 13. Also has a sequential let, called let*, that evaluates the bindings from left to right. (let* ((a 5) (b (+ a 3))) (* a b)) is equivalent to (let ( ...
... Expression (let ((a 5) (b 8)) (+ a b)) is an abbreviation of the function application ((lambda (a b) (+ a b)) 5 8); Both expressions return the value 13. Also has a sequential let, called let*, that evaluates the bindings from left to right. (let* ((a 5) (b (+ a 3))) (* a b)) is equivalent to (let ( ...
lec4
... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...
... To evaluate (E1 E2 ... En), recursively evaluate E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various spec ...
This article discusses the programming language LISP. The
... n, f (x1 ; x2 ; : : : ; xn ). Here, x1; : : : ; xn are called the formal arguments and when we actually wish to evaluate the function f we provide the `actual arguments' (like 3 and 4 for + above) and evaluate the function to get the resulting answer. These kind of functions are part of most program ...
... n, f (x1 ; x2 ; : : : ; xn ). Here, x1; : : : ; xn are called the formal arguments and when we actually wish to evaluate the function f we provide the `actual arguments' (like 3 and 4 for + above) and evaluate the function to get the resulting answer. These kind of functions are part of most program ...
![Scheme [PPT]](http://s1.studyres.com/store/data/000434604_1-ff9167cda1c43083f470d57127811028-300x300.png)
Scheme [PPT]
... • map – Takes as arguments a function and a sequence of lists – There must be as many lists as arguments of the function, and lists must have the same length – Applies the function on corresponding sets of elements from the lists – Returns all the results in a list f (E1 E2 ...... En) ((f E1) (f E ...
... • map – Takes as arguments a function and a sequence of lists – There must be as many lists as arguments of the function, and lists must have the same length – Applies the function on corresponding sets of elements from the lists – Returns all the results in a list f (E1 E2 ...... En) ((f E1) (f E ...
Introduction to Emacs and Emacs lisp
... of one set to another set Described by an expression or a table The evaluation order is controlled by recursion and conditional expressions ...
... of one set to another set Described by an expression or a table The evaluation order is controlled by recursion and conditional expressions ...
Functional Programming, ML, and the λ
... Programming in Standard ML • The SML prompt lets you type either a term or a declaration that binds a variable to a term • Running an ML program is just evaluating a term – The ML evaluator takes the left-most expression that is not a value and reduces it to some simpler expression. Eventually the ...
... Programming in Standard ML • The SML prompt lets you type either a term or a declaration that binds a variable to a term • Running an ML program is just evaluating a term – The ML evaluator takes the left-most expression that is not a value and reduces it to some simpler expression. Eventually the ...
A Contraction-free and Cut-free Sequent Calculus for
... ponens and the rule of necessitation; and (iii) at least one axiom schema or inference rule for each program operator. What about Gentzen calculi for propositional dynamic logic? In this case the situation is not so positive. As far as we know only two sequent calculi have been proposed; namely, the ...
... ponens and the rule of necessitation; and (iii) at least one axiom schema or inference rule for each program operator. What about Gentzen calculi for propositional dynamic logic? In this case the situation is not so positive. As far as we know only two sequent calculi have been proposed; namely, the ...
Elements of Finite Model Theory
... no constant depth polynomial size family of circuits that computes parity. The Chapter also introduces parametric complexity in application to the modelchecking problem, which is of special interest from the database perspective, where typically queries are very small compared to the databases again ...
... no constant depth polynomial size family of circuits that computes parity. The Chapter also introduces parametric complexity in application to the modelchecking problem, which is of special interest from the database perspective, where typically queries are very small compared to the databases again ...
3.1.3 Subformulas
... 2. If ¬G ∈ S(F ) , then G ∈ S(F ). 3. If (G1 ◦ G2 ) ∈ S(F ) , then G1 , G2 ∈ S(F ). It will be shown in Exercise 3.4 that such a smallest set exists. As an example, let F be the formula ¬((p1 → p2 ) ∨ p1 ). Then we have S(F ) = {¬((p1 → p2 ) ∨ p1 ), ((p1 → p2 ) ∨ p1 ), (p1 → p2 ), p1 , p2 } (see als ...
... 2. If ¬G ∈ S(F ) , then G ∈ S(F ). 3. If (G1 ◦ G2 ) ∈ S(F ) , then G1 , G2 ∈ S(F ). It will be shown in Exercise 3.4 that such a smallest set exists. As an example, let F be the formula ¬((p1 → p2 ) ∨ p1 ). Then we have S(F ) = {¬((p1 → p2 ) ∨ p1 ), ((p1 → p2 ) ∨ p1 ), (p1 → p2 ), p1 , p2 } (see als ...
Unit-1-B - WordPress.com
... Mathematical Reasoning We need mathematical reasoning to determine whether a mathematical argument is correct or incorrect Mathematical reasoning is important for artificial intelligence systems to reach a conclusion from knowledge and facts. We can use a proof to demonstrate that a particular stat ...
... Mathematical Reasoning We need mathematical reasoning to determine whether a mathematical argument is correct or incorrect Mathematical reasoning is important for artificial intelligence systems to reach a conclusion from knowledge and facts. We can use a proof to demonstrate that a particular stat ...
A Calculus for Type Predicates and Type Coercion
... – f (t1 , . . . , tn ) ∈ TA for any function symbol f : A1 , . . . , An → A, and terms ti ∈ TAi with Ai Ai for i = 1, . . . , n, – (A)t ∈ TA for any term t ∈ TA where A is an arbitrary type. We write the static type of t as σ(t) := A for any term t ∈ TA . A term (A)t is a type coercion, also c ...
... – f (t1 , . . . , tn ) ∈ TA for any function symbol f : A1 , . . . , An → A, and terms ti ∈ TAi with Ai Ai for i = 1, . . . , n, – (A)t ∈ TA for any term t ∈ TA where A is an arbitrary type. We write the static type of t as σ(t) := A for any term t ∈ TA . A term (A)t is a type coercion, also c ...
![arXiv:1410.5037v2 [cs.LO] 18 Jun 2016](http://s1.studyres.com/store/data/007883898_2-29c425582568c0e0d15c3d815896c9cf-300x300.png)
arXiv:1410.5037v2 [cs.LO] 18 Jun 2016
... The satisfiability problem of two-variable logic FO2 was shown to be NEXPTIME-complete in [9]. The extension of two-variable logic with counting quantifiers, FOC2 , was proved decidable in [10,21], and it was subsequently shown to be NEXPTIME-complete in [22]. Research on extensions and variants of ...
... The satisfiability problem of two-variable logic FO2 was shown to be NEXPTIME-complete in [9]. The extension of two-variable logic with counting quantifiers, FOC2 , was proved decidable in [10,21], and it was subsequently shown to be NEXPTIME-complete in [22]. Research on extensions and variants of ...
Basic Metatheory for Propositional, Predicate, and Modal Logic
... whether every truth function is expressed by some formula of L P . The issue here hinges on the connectives of L P . A set of connectives in an interpreted language (i.e., a language together with its semantics) for propositional logic is said to be adequate iff every truth function can be expressed ...
... whether every truth function is expressed by some formula of L P . The issue here hinges on the connectives of L P . A set of connectives in an interpreted language (i.e., a language together with its semantics) for propositional logic is said to be adequate iff every truth function can be expressed ...
General Dynamic Dynamic Logic
... logic [7,11,12,20]. A significant difference from the epistemic setting is the need to describe dynamic operators that change the relational structure of the underlying model, not just the size of its domain (announcement) or the propositional valuations (real-world change). For example, if one mode ...
... logic [7,11,12,20]. A significant difference from the epistemic setting is the need to describe dynamic operators that change the relational structure of the underlying model, not just the size of its domain (announcement) or the propositional valuations (real-world change). For example, if one mode ...
Judgment and consequence relations
... Also, given (4), T is maximally consistent. In this definition we consider truth in the classical sense. A proposition is either true or false. If it is rejected, that is, if 0T ϕ this is because the proposition is false. So, no subjective element enters here. Truth is independent of whether we know ...
... Also, given (4), T is maximally consistent. In this definition we consider truth in the classical sense. A proposition is either true or false. If it is rejected, that is, if 0T ϕ this is because the proposition is false. So, no subjective element enters here. Truth is independent of whether we know ...
Functional Programming
... may stop with the weak head normal form λy.(λx.x y) or with the normal form λy.y depending on the convention we follow. When viewing Lambda calculus as a conventional programming language we may stop with the weak head normal form λy.(λx.x y). When investigating theoretically the value of the expres ...
... may stop with the weak head normal form λy.(λx.x y) or with the normal form λy.y depending on the convention we follow. When viewing Lambda calculus as a conventional programming language we may stop with the weak head normal form λy.(λx.x y). When investigating theoretically the value of the expres ...
slides (modified) - go here for webmail
... A proof uses a given set of inference rules and axioms. This is called the proof system. Let H be a proof system. ` H φ means: there is a proof of φ in system H whose premises are included in `H is called the provability relation. ...
... A proof uses a given set of inference rules and axioms. This is called the proof system. Let H be a proof system. ` H φ means: there is a proof of φ in system H whose premises are included in `H is called the provability relation. ...