First-Order Logic - Sonoma State University
... – if Pj and ~Qk unify with substitution list Theta, – then derive the resolvent sentence: subst(Theta, P1 v ... v Pj-1 v Pj+1 v ... v Pn v Q1 v ... ...
... – if Pj and ~Qk unify with substitution list Theta, – then derive the resolvent sentence: subst(Theta, P1 v ... v Pj-1 v Pj+1 v ... v Pn v Q1 v ... ...
24.241 Logic I Problem set 04 solutions
... Γ and the conclusion of α is P (I’m using ‘α’ so you don’t confuse it with a sentence letter of SL, but you can use whatever you like). 1. α is valid in SD iff there is an SD derivation that has the members of Γ as primary assumptions and P in the scope of those assumptions only (by definition of ‘va ...
... Γ and the conclusion of α is P (I’m using ‘α’ so you don’t confuse it with a sentence letter of SL, but you can use whatever you like). 1. α is valid in SD iff there is an SD derivation that has the members of Γ as primary assumptions and P in the scope of those assumptions only (by definition of ‘va ...
Combinatorial structures and processing in Neural Blackboard
... are ‘in situ’ [4]. That is, wherever a concept is activated it always consists of the activation of the assembly of that concept or a part of it. In this view, it is not possible to make a copy of a concept representation and store it elsewhere in the brain to, for example, create a combinatorial st ...
... are ‘in situ’ [4]. That is, wherever a concept is activated it always consists of the activation of the assembly of that concept or a part of it. In this view, it is not possible to make a copy of a concept representation and store it elsewhere in the brain to, for example, create a combinatorial st ...
Lesson 12
... There is a subtle difference between entailment and inference. Version 2 CSE IIT, Kharagpur ...
... There is a subtle difference between entailment and inference. Version 2 CSE IIT, Kharagpur ...
P(x)
... general unifier (mgu), i.e., a shortest length substitution list that makes the two literals match. – (In general, there is not a unique minimum length substitution list, but unify returns one of them.) ...
... general unifier (mgu), i.e., a shortest length substitution list that makes the two literals match. – (In general, there is not a unique minimum length substitution list, but unify returns one of them.) ...
A Recursively Axiomatizable Subsystem of Levesque`s Logic of Only
... valid sentences, we shall attempt to axiomatize a subset of it, namely those valid in a wider class of models. We consider the same language but a more general de nition of model. In order to axiomatize the largest possible set of valid sentences we shall try to keep our de nition of models as close ...
... valid sentences, we shall attempt to axiomatize a subset of it, namely those valid in a wider class of models. We consider the same language but a more general de nition of model. In order to axiomatize the largest possible set of valid sentences we shall try to keep our de nition of models as close ...
P(x) - Carnegie Mellon School of Computer Science
... general unifier (mgu), i.e., a shortest length substitution list that makes the two literals match. – (In general, there is not a unique minimum length substitution list, but unify returns one of them.) ...
... general unifier (mgu), i.e., a shortest length substitution list that makes the two literals match. – (In general, there is not a unique minimum length substitution list, but unify returns one of them.) ...
An Abridged Report - Association for the Advancement of Artificial
... balance towards consistency-based approaches is the application of logics of knowledge and belief [Halpern and to appear, 1987].3 Although Moses, 19851 and [McArthur, 1This research was made possible in part by a grant from the Natural Sciences and Engineering Research Council of Canada. Thanks also ...
... balance towards consistency-based approaches is the application of logics of knowledge and belief [Halpern and to appear, 1987].3 Although Moses, 19851 and [McArthur, 1This research was made possible in part by a grant from the Natural Sciences and Engineering Research Council of Canada. Thanks also ...
![overhead 8/singular sentences [ov]](http://s1.studyres.com/store/data/009258618_1-2a98e952bde8fd34c716ae0716ce6df4-300x300.png)
overhead 8/singular sentences [ov]
... - these words are similar to names in that they function grammatically as the subjects of these sentences - but these words are different from names in that they don't refer: "something" and "everything" don't refer to particular things or people; obviously "nothing" doesn't refer ...
... - these words are similar to names in that they function grammatically as the subjects of these sentences - but these words are different from names in that they don't refer: "something" and "everything" don't refer to particular things or people; obviously "nothing" doesn't refer ...
P Q
... (i.e.: is there a world in which this sentence is satisfied?) IN OTHER WORDS: Is there such truth assignment of all propositional symbols occurring in the sentence, which make it to be assigned T? OUTPUT: YES or NO ...
... (i.e.: is there a world in which this sentence is satisfied?) IN OTHER WORDS: Is there such truth assignment of all propositional symbols occurring in the sentence, which make it to be assigned T? OUTPUT: YES or NO ...
In defence of an argument against truthmaker maximalism
... outright inconsistency of S. And needless to say, nothing can be proved by logically inconsistent sentences. On the other hand, if S is not short (because we assume, for example, that ‘short’ means ‘consisting of no more than 5 words’), S is simply true and does not “establish (the negation of) just ...
... outright inconsistency of S. And needless to say, nothing can be proved by logically inconsistent sentences. On the other hand, if S is not short (because we assume, for example, that ‘short’ means ‘consisting of no more than 5 words’), S is simply true and does not “establish (the negation of) just ...
Variations on a Montagovian Theme
... standard vocabulary of arithmetic, so that it can express things like 2 + 2 = 4. A theory is arithmetically sound if it does not contain any arithmetical falsehoods (like 2 + 2 = 5). The set L of logical truths, for example, is arithmetically sound, but it also contains very few arithmetical truths. ...
... standard vocabulary of arithmetic, so that it can express things like 2 + 2 = 4. A theory is arithmetically sound if it does not contain any arithmetical falsehoods (like 2 + 2 = 5). The set L of logical truths, for example, is arithmetically sound, but it also contains very few arithmetical truths. ...
Chapter 5: Methods of Proof for Boolean Logic
... TT-contradictory. This will require some extra footwork in cases in which we have other kinds of contradictions. § 5.4 Arguments with inconsistent premises If a set of premises is inconsistent, any argument having those premises is valid. (If the premises are inconsistent, there is no possible circu ...
... TT-contradictory. This will require some extra footwork in cases in which we have other kinds of contradictions. § 5.4 Arguments with inconsistent premises If a set of premises is inconsistent, any argument having those premises is valid. (If the premises are inconsistent, there is no possible circu ...
IM_FA16-03-PredicateLogic
... • Formation rules and valuation rules, are clearly in the metalanguage. • And so, less obviously, are equivalence rules • The actual well-formed expressions of SL and PL are in the object language. • The metalanguage, more or less carefully written logic-like English, is not formally defined, with t ...
... • Formation rules and valuation rules, are clearly in the metalanguage. • And so, less obviously, are equivalence rules • The actual well-formed expressions of SL and PL are in the object language. • The metalanguage, more or less carefully written logic-like English, is not formally defined, with t ...
CHAPTER 1. SENTENTIAL LOGIC 1. Introduction In sentential logic
... Using them we can define more connectives, for example 2 is prime iff 2 is odd can be defined as (If 2 is prime then 2 is odd) and (if 2 is odd then 2 is prime). The truth value of any compound sentence is determined completely by the truth values of its component parts. For example, assuming 2, 7, ...
... Using them we can define more connectives, for example 2 is prime iff 2 is odd can be defined as (If 2 is prime then 2 is odd) and (if 2 is odd then 2 is prime). The truth value of any compound sentence is determined completely by the truth values of its component parts. For example, assuming 2, 7, ...
10a
... Example: “It's raining or it's not raining” • An inconsistent sentence or contradiction is a sentence that is False under all interpretations. The world is never like what it describes, as in “It's raining and it's not raining.” • P entails Q, written P |= Q, means that whenever P is True, so is Q – ...
... Example: “It's raining or it's not raining” • An inconsistent sentence or contradiction is a sentence that is False under all interpretations. The world is never like what it describes, as in “It's raining and it's not raining.” • P entails Q, written P |= Q, means that whenever P is True, so is Q – ...
An Automata Theoretic Decision Procedure for the Propositional Mu
... is consistent with the semantics for greatest fixpoints (this explains why pX. X - false and vX. X E true). Disjunctions p v q and existential program sentences (A )p introduce a complication; termination of the evaluation process depends on the choice of disjunct or edge used to satisfy such senten ...
... is consistent with the semantics for greatest fixpoints (this explains why pX. X - false and vX. X E true). Disjunctions p v q and existential program sentences (A )p introduce a complication; termination of the evaluation process depends on the choice of disjunct or edge used to satisfy such senten ...
Propositional Logic
... contained. Also, logical reasoning methods are designed to work no matter what meanings or values are assigned to the logical “variables” used in sentences. Although the values assigned to variables are not crucial in the sense just described, in talking about logic itself, it is sometimes useful t ...
... contained. Also, logical reasoning methods are designed to work no matter what meanings or values are assigned to the logical “variables” used in sentences. Although the values assigned to variables are not crucial in the sense just described, in talking about logic itself, it is sometimes useful t ...
PROPERTIES PRESERVED UNDER ALGEBRAIC
... Further related results are given by K. Bing, 1955. It seems probable t h a t every universal-existential sentence preserved under direct products is equivalent to a Horn sentence ; but an example by Chang and Anne Morel, of which we shall speak later, shows that the analogous statement for existent ...
... Further related results are given by K. Bing, 1955. It seems probable t h a t every universal-existential sentence preserved under direct products is equivalent to a Horn sentence ; but an example by Chang and Anne Morel, of which we shall speak later, shows that the analogous statement for existent ...
Inference in First
... than) an existing sentence to keep the KB small • Like factoring, this is just removing things that merely clutter up the space and will not affect the final result • E.g., if P(x) is already in the KB, adding P(A) makes no sense – P(x) is a superset of P(A) • Likewise adding P(A) Q(B) would add n ...
... than) an existing sentence to keep the KB small • Like factoring, this is just removing things that merely clutter up the space and will not affect the final result • E.g., if P(x) is already in the KB, adding P(A) makes no sense – P(x) is a superset of P(A) • Likewise adding P(A) Q(B) would add n ...
Logic and Reasoning
... • Proof can be viewed as a search problem The basic search algorithms that we saw before can be used here – State: KB – Successor: Apply inference to KB to obtain new sentences – Solution: Sequence of inferences to goal sentence. If the inference algorithm is sound, then this is guaranteed to esta ...
... • Proof can be viewed as a search problem The basic search algorithms that we saw before can be used here – State: KB – Successor: Apply inference to KB to obtain new sentences – Solution: Sequence of inferences to goal sentence. If the inference algorithm is sound, then this is guaranteed to esta ...
True
... • Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated • We say m is a model of a sentence α if α is true in m • M(α) is the set of all models of α • Then KB ╞ α iff M(KB) ⊆ M(α) ...
... • Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated • We say m is a model of a sentence α if α is true in m • M(α) is the set of all models of α • Then KB ╞ α iff M(KB) ⊆ M(α) ...
ppt
... • Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated • We say m is a model of a sentence α if α is true in m • M(α) is the set of all models of α • Then KB ╞ α iff M(KB) M(α) – E.g. KB = Giants won and Reds ...
... • Logicians typically think in terms of models, which are formally structured worlds with respect to which truth can be evaluated • We say m is a model of a sentence α if α is true in m • M(α) is the set of all models of α • Then KB ╞ α iff M(KB) M(α) – E.g. KB = Giants won and Reds ...
