F - Teaching-WIKI
... • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sentence that is True under all interpretations, no matter what the world is actually like or how the semantics are defined (ex ...
... • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sentence that is True under all interpretations, no matter what the world is actually like or how the semantics are defined (ex ...
Display version
... Here are some useful functions for screen output: (display X) (newline) (printf format args...) The catch-all format flag is ˜a. (Note: Strings in Scheme are made using double quotes, like "This is a string".) ...
... Here are some useful functions for screen output: (display X) (newline) (printf format args...) The catch-all format flag is ˜a. (Note: Strings in Scheme are made using double quotes, like "This is a string".) ...
Speaking Logic - SRI International
... all A in Γ, and M |= ¬B for all B ∈ ∆. In LK , any countermodel of some premise of a rule is also a countermodel for the conclusion. We can then show that a non-provable sequent Γ ` ∆ has a countermodel. Each non-Cut rule has premises that are simpler than its conclusion. By applying the rules start ...
... all A in Γ, and M |= ¬B for all B ∈ ∆. In LK , any countermodel of some premise of a rule is also a countermodel for the conclusion. We can then show that a non-provable sequent Γ ` ∆ has a countermodel. Each non-Cut rule has premises that are simpler than its conclusion. By applying the rules start ...
On the specification of sequent systems
... be used to draw conclusions about the object-level proof systems. More specifically, in [MP02], the authors present a decision procedure for determining if one encoded proof system is derivable from another. In the same paper, necessary conditions were presented (together with a decision procedure) ...
... be used to draw conclusions about the object-level proof systems. More specifically, in [MP02], the authors present a decision procedure for determining if one encoded proof system is derivable from another. In the same paper, necessary conditions were presented (together with a decision procedure) ...
Boolean unification with predicates
... 2.1 Second-order unification Instead of working modulo an equational theory, the standard (i.e. syntactic first-order) unification problem has also been extended to allow for higher-order variables. Second-order unification permits, in addition to individual variables, also function variables and as ...
... 2.1 Second-order unification Instead of working modulo an equational theory, the standard (i.e. syntactic first-order) unification problem has also been extended to allow for higher-order variables. Second-order unification permits, in addition to individual variables, also function variables and as ...
chapter1p3 - WordPress.com
... Let us look at the examples considered earlier. In the first one there are two variables and the minterms occurring in the expression correspond to 0, 2 and 3 and this is written as 0, 2, 3. In the second example the minterms correspond to 7, 6, 3, 1 respectively and the expression is written as 1 ...
... Let us look at the examples considered earlier. In the first one there are two variables and the minterms occurring in the expression correspond to 0, 2 and 3 and this is written as 0, 2, 3. In the second example the minterms correspond to 7, 6, 3, 1 respectively and the expression is written as 1 ...
Concepts of Programming Languages A Brief Intro to Programming
... - is both a highly optimising compiler as well as an interactive interpreter ...
... - is both a highly optimising compiler as well as an interactive interpreter ...
pl10ch15 - ODU Computer Science
... architecture of the machines on which programs will run Copyright © 2012 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2012 Addison-Wesley. All rights reserved. ...
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 ...
Kripke Models of Transfinite Provability Logic
... Kripke frames for the closed fragment of GLPω , which contains no propositional variables (only ⊥). This fragment, which we denote GLP0ω , is still expressive enough to be used in Beklemishev’s ordinal analysis. Our goal is to extend Ignatiev’s construction for GLP0ω to GLP0Λ , where Λ is an arbitra ...
... Kripke frames for the closed fragment of GLPω , which contains no propositional variables (only ⊥). This fragment, which we denote GLP0ω , is still expressive enough to be used in Beklemishev’s ordinal analysis. Our goal is to extend Ignatiev’s construction for GLP0ω to GLP0Λ , where Λ is an arbitra ...
Is `structure` a clear notion? - University of Illinois at Chicago
... notion of a formal system. But it is a crucial one9 and one that is often overlooked by non-logicians. From the standpoint of formalization, fixing the vocabulary is a first step, singling out the ‘primitive concepts’. Considerable reflection from both mathematical and philosophical standpoints may ...
... notion of a formal system. But it is a crucial one9 and one that is often overlooked by non-logicians. From the standpoint of formalization, fixing the vocabulary is a first step, singling out the ‘primitive concepts’. Considerable reflection from both mathematical and philosophical standpoints may ...
Functional Programming
... • Pure functional programming is state-free: no assignment statements. • Programs in pure functional languages consist of composite functions; output of each function is input to another. • Today, most functional languages have some imperative statements. ...
... • Pure functional programming is state-free: no assignment statements. • Programs in pure functional languages consist of composite functions; output of each function is input to another. • Today, most functional languages have some imperative statements. ...
Functional Programming in Scheme
... The value assigned to X depends on the evaluation order of the expression F(&X)+ ++X for any initial value a of X different than 0. The result of the expression F(&X) + ++X is 1, for the left-to-right evaluation, and a+1 if the evaluation is right-to-left. Banning side effects have important consequ ...
... The value assigned to X depends on the evaluation order of the expression F(&X)+ ++X for any initial value a of X different than 0. The result of the expression F(&X) + ++X is 1, for the left-to-right evaluation, and a+1 if the evaluation is right-to-left. Banning side effects have important consequ ...
this PDF file
... As is known, the real difficulty in proving the admissibility of γ in relevant logics lies in proving that every prime theory containing all theorems (of the logic in question) and lacking a given formula has a negation-consistent, complete subtheory with all theorems (of the logic in question) lack ...
... As is known, the real difficulty in proving the admissibility of γ in relevant logics lies in proving that every prime theory containing all theorems (of the logic in question) and lacking a given formula has a negation-consistent, complete subtheory with all theorems (of the logic in question) lack ...
CS 399: Constructive Logic Final Exam (Sample Solution) Name Instructions
... “exclusive or.” A¯B is provable exactly when either A or B is provable and the other is refutable. We could give a definition of ¯ in terms of other connectives as A ¯ B ≡ (A ∧ ¬B) ∨ (¬A ∧ B). But, we will give a direct definition for A ¯ B using intro and elim rules that capture the informal meanin ...
... “exclusive or.” A¯B is provable exactly when either A or B is provable and the other is refutable. We could give a definition of ¯ in terms of other connectives as A ¯ B ≡ (A ∧ ¬B) ∨ (¬A ∧ B). But, we will give a direct definition for A ¯ B using intro and elim rules that capture the informal meanin ...
Theorems for free! - Computing Science
... [BFSS87, FGSS88], from whom I have taken the name \parametricity". So far as I am aware, all uses of parametricity to date have been \general": they say something about possible implementations of the polymorphic lambda calculus (e.g. that the implementation is correct independent of the representat ...
... [BFSS87, FGSS88], from whom I have taken the name \parametricity". So far as I am aware, all uses of parametricity to date have been \general": they say something about possible implementations of the polymorphic lambda calculus (e.g. that the implementation is correct independent of the representat ...
ML Functions - Welcome to Computer Science
... ML also limits defined functions to only take a single parameter, however, this parameter may be a tuple, or a ‘unit’ (the empty set). ML is typically run in an interpretive manner. ...
... ML also limits defined functions to only take a single parameter, however, this parameter may be a tuple, or a ‘unit’ (the empty set). ML is typically run in an interpretive manner. ...
A(x)
... completeness of the 1st order predicate calculus, which was expected. He even proved the strong completeness: if SA |= T then SA |– T (SA – a set of assumptions). But Hilbert wanted more: he supposed that all the truths of mathematics can be proved in this mechanic finite way. That is, that a theory ...
... completeness of the 1st order predicate calculus, which was expected. He even proved the strong completeness: if SA |= T then SA |– T (SA – a set of assumptions). But Hilbert wanted more: he supposed that all the truths of mathematics can be proved in this mechanic finite way. That is, that a theory ...
Systems of modal logic - Department of Computing
... (iii) We have to show that ΣF contains PL and is closed under MP and US. The first two are straightforward and are left as an exercise (tutorial sheet). To show closure under US is not difficult but is rather long and fiddly so details omitted here. The basic idea is simple enough. Blackburn et al p ...
... (iii) We have to show that ΣF contains PL and is closed under MP and US. The first two are straightforward and are left as an exercise (tutorial sheet). To show closure under US is not difficult but is rather long and fiddly so details omitted here. The basic idea is simple enough. Blackburn et al p ...
Logic programming slides
... (So in this sense SLD-resolution is complete.) Counterexamples for arbitrary sets of predicate logical sentences = {Pa, x Px} has a model but no minimal Herbrand model. The Herbrand universe of is {a}, but no model on this domain satisfies . ' = {Pa Qa} has two minimal Herbrand models ...
... (So in this sense SLD-resolution is complete.) Counterexamples for arbitrary sets of predicate logical sentences = {Pa, x Px} has a model but no minimal Herbrand model. The Herbrand universe of is {a}, but no model on this domain satisfies . ' = {Pa Qa} has two minimal Herbrand models ...
16 - Institute for Logic, Language and Computation
... (So in this sense SLD-resolution is complete.) Counterexamples for arbitrary sets of predicate logical sentences = {Pa, x Px} has a model but no minimal Herbrand model. The Herbrand universe of is {a}, but no model on this domain satisfies . ' = {Pa Qa} has two minimal Herbrand models ...
... (So in this sense SLD-resolution is complete.) Counterexamples for arbitrary sets of predicate logical sentences = {Pa, x Px} has a model but no minimal Herbrand model. The Herbrand universe of is {a}, but no model on this domain satisfies . ' = {Pa Qa} has two minimal Herbrand models ...
Answer Sets for Propositional Theories
... Note that, even if (5) is classically equivalent to (7), they are not equivalent in the logic of here-and-there. This shows that it is generally incorrect to “move” a negation from a binary relation symbol (such as 6=) in front of the aggregate as the unary connective ¬. Some properties of aggregate ...
... Note that, even if (5) is classically equivalent to (7), they are not equivalent in the logic of here-and-there. This shows that it is generally incorrect to “move” a negation from a binary relation symbol (such as 6=) in front of the aggregate as the unary connective ¬. Some properties of aggregate ...
PROPOSITIONAL LOGIC 1 Propositional Logic - Glasnost!
... leap forward in both logic and mathematics. In 1847 Boole published his first book, The Mathematical Analysis of Logic. As a result of this publication and on the recommendation of many of the leading British mathematicians of the day, Boole was appointed first Professor of Mathematics at the newly ...
... leap forward in both logic and mathematics. In 1847 Boole published his first book, The Mathematical Analysis of Logic. As a result of this publication and on the recommendation of many of the leading British mathematicians of the day, Boole was appointed first Professor of Mathematics at the newly ...