Wumpus world in Propositional logic.
... map (as opposed to a rectangular grid like the even older Star Trek games). • In this respect, as in the dungeon-like setting and its terse, amusing messages, it prefigured ADVENT and Zork. •It was directly ancestral to both. – (Zork acknowledged this heritage by including a super-bat colony.) – Tod ...
... map (as opposed to a rectangular grid like the even older Star Trek games). • In this respect, as in the dungeon-like setting and its terse, amusing messages, it prefigured ADVENT and Zork. •It was directly ancestral to both. – (Zork acknowledged this heritage by including a super-bat colony.) – Tod ...
Canad. Math. Bull. Vol. 24 (2), 1981 INDEPENDENT SETS OF
... §0. Introduction. A set of sentences T is called independent if for every
... §0. Introduction. A set of sentences T is called independent if for every
Beautifying Gödel - Department of Computer Science
... Given the reflexive axiom of equality, a formalist is willing to accept 0÷0 = 0÷0 as a theorem of NT. He is not concerned with what mathematical object is referred to by 0÷0 . He is likewise willing to accept |– “)+x=(” as a sentence of TT , though it is not a theorem. We defined |– as a predicate o ...
... Given the reflexive axiom of equality, a formalist is willing to accept 0÷0 = 0÷0 as a theorem of NT. He is not concerned with what mathematical object is referred to by 0÷0 . He is likewise willing to accept |– “)+x=(” as a sentence of TT , though it is not a theorem. We defined |– as a predicate o ...
An Abridged Report - Association for the Advancement of Artificial
... operators are called basic. We will use CI!and p to range over sentences, cr to range over the subjective sentences only, and 4 and 1c, to range over the objective sentences only. Finally, cr: is used to name the formula consisting of Q with ...
... operators are called basic. We will use CI!and p to range over sentences, cr to range over the subjective sentences only, and 4 and 1c, to range over the objective sentences only. Finally, cr: is used to name the formula consisting of Q with ...
Keep Changing Your Beliefs, Aiming for the Truth
... are known as special cases of Halpern’s ‘‘preferential models’’ (Halpern 2003), Grove’s ‘‘sphere’’ models (Grove 1988), Spohn’s ordinal-ranked models (Spohn 1988) and Board’s ‘‘belief-revision structures’’ (Board 2002). As models we use pointed plausibility models, which are plausibility structures ...
... are known as special cases of Halpern’s ‘‘preferential models’’ (Halpern 2003), Grove’s ‘‘sphere’’ models (Grove 1988), Spohn’s ordinal-ranked models (Spohn 1988) and Board’s ‘‘belief-revision structures’’ (Board 2002). As models we use pointed plausibility models, which are plausibility structures ...
Propositional Logic Syntax of Propositional Logic
... • checking a set of sentences for satisfiability is NP-complete – but there are some circumstances where the proof only involves a small subset of the KB, so can do some of the work in polynomial time – if a KB is monotonic (i.e., even if we add new sentences to a KB, all the sentences entailed by t ...
... • checking a set of sentences for satisfiability is NP-complete – but there are some circumstances where the proof only involves a small subset of the KB, so can do some of the work in polynomial time – if a KB is monotonic (i.e., even if we add new sentences to a KB, all the sentences entailed by t ...
Advanced Topics in Propositional Logic
... 1.Start out as though you were going to build a truth table, by listing all the atomic sentences in in a row, followed by S. But do not write T or F beneath any of them yet. 2.If there is a conjunct of the form Ai, assign T to Ai, i.e., write T in the reference column under Ai. Repeat this as long a ...
... 1.Start out as though you were going to build a truth table, by listing all the atomic sentences in in a row, followed by S. But do not write T or F beneath any of them yet. 2.If there is a conjunct of the form Ai, assign T to Ai, i.e., write T in the reference column under Ai. Repeat this as long a ...
WUMPUS
... • This game appears to have been the first to use a non-random graph-structured map (as opposed to a rectangular grid like the even older Star Trek games). • In this respect, as in the dungeon-like setting and its terse, amusing messages, it prefigured ADVENT and Zork. •It was directly ancestral to ...
... • This game appears to have been the first to use a non-random graph-structured map (as opposed to a rectangular grid like the even older Star Trek games). • In this respect, as in the dungeon-like setting and its terse, amusing messages, it prefigured ADVENT and Zork. •It was directly ancestral to ...
The disjunction introduction rule: Syntactic and semantics
... data that allow us to choose one of them. Orenes and Johnson-Laird´s (2012) paper seems to give such data. The results of an experiment carried out by them show that, although it is true that, in many cases, people do not apply the disjunction introduction rule, there are also cases in which they do ...
... data that allow us to choose one of them. Orenes and Johnson-Laird´s (2012) paper seems to give such data. The results of an experiment carried out by them show that, although it is true that, in many cases, people do not apply the disjunction introduction rule, there are also cases in which they do ...
True
... • Problem-solving agents were very inflexible: hard code every possible state. • Search is almost always exponential in the number of states. • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
... • Problem-solving agents were very inflexible: hard code every possible state. • Search is almost always exponential in the number of states. • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
Is the Liar Sentence Both True and False? - NYU Philosophy
... with acceptance. To a Þrst approximation anyway, accepting A is having a high degree of belief in it; say a degree of belief over a certain threshold T , which may depend on context but must be greater than 12 . (Degrees of belief are assumed to be real numbers in the interval [0, 1].) To the same ...
... with acceptance. To a Þrst approximation anyway, accepting A is having a high degree of belief in it; say a degree of belief over a certain threshold T , which may depend on context but must be greater than 12 . (Degrees of belief are assumed to be real numbers in the interval [0, 1].) To the same ...
ppt
... • Problem-solving agents were very inflexible: hard code every possible state. • Search is almost always exponential in the number of states. • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
... • Problem-solving agents were very inflexible: hard code every possible state. • Search is almost always exponential in the number of states. • Problem solving agents cannot infer unobserved information. • We want an algorithm that reasons in a way that resembles reasoning in humans. ...
On Perfect Introspection with Quantifying-in
... knowledge about themselves. In other words, while such agents may have incomplete beliefs about the world, they always have complete knowledge about their own beliefs by way of their ability to introspect. Thus it seems that the beliefs of a perfectly introspective agent should be completely determi ...
... knowledge about themselves. In other words, while such agents may have incomplete beliefs about the world, they always have complete knowledge about their own beliefs by way of their ability to introspect. Thus it seems that the beliefs of a perfectly introspective agent should be completely determi ...
A unified account of causal relata
... consists in a physical object's acquiring a property which it did not possess at an earlier time or its losing a property it did possess at an earlier time, an event happens over a period of time. A state of affairs, on the other hand, may be instantaneous.) Moreover, events are not only changes, th ...
... consists in a physical object's acquiring a property which it did not possess at an earlier time or its losing a property it did possess at an earlier time, an event happens over a period of time. A state of affairs, on the other hand, may be instantaneous.) Moreover, events are not only changes, th ...
Completeness of the predicate calculus
... The second thing we need to do is to precisify the notion of a sentence of predicate logic. Suppose that we have a fixed family R of predicate symbols, and a fixed family C of constant symbols. Then we define the set Σ of sentences inductively as follows: 1. Base case: If R is an n-ary relation sym ...
... The second thing we need to do is to precisify the notion of a sentence of predicate logic. Suppose that we have a fixed family R of predicate symbols, and a fixed family C of constant symbols. Then we define the set Σ of sentences inductively as follows: 1. Base case: If R is an n-ary relation sym ...
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. ...
Abstract for ‘Consequentialism’ 1 Inferentialism vs referentialism David Ripley
... the meaning of the conditional, including any truth conditions it may or may not have. By contrast, referentialists hold that meanings are determined by what is represented; as applied to logical constants, this is often taken to be a matter of truth conditions. For example, a representationalist co ...
... the meaning of the conditional, including any truth conditions it may or may not have. By contrast, referentialists hold that meanings are determined by what is represented; as applied to logical constants, this is often taken to be a matter of truth conditions. For example, a representationalist co ...
slides - National Taiwan University
... |= is about semantics, rather than syntax For Σ = ∅, we have ∅ |= τ , simply written |= τ . It says every truth assignment satisfies τ . In this case, τ is a tautology. ...
... |= is about semantics, rather than syntax For Σ = ∅, we have ∅ |= τ , simply written |= τ . It says every truth assignment satisfies τ . In this case, τ is a tautology. ...
Propositional Logic
... Two important properties for inference Soundness: If KB |- Q then KB |= Q – If Q is derived from a set of sentences KB using a given set of rules of inference, then Q is entailed by KB. – Hence, inference produces only real entailments, or any sentence that follows deductively from the premises is ...
... Two important properties for inference Soundness: If KB |- Q then KB |= Q – If Q is derived from a set of sentences KB using a given set of rules of inference, then Q is entailed by KB. – Hence, inference produces only real entailments, or any sentence that follows deductively from the premises is ...
Sidestepping the holes of holism
... and points to a possible source of the lack of clarity in holistic doctrines – namely the refusal of making the degree of dependence explicit. This last feature is especially important if we keep in mind that some holistic theories seem to be trivial in character – if, for example, by “being an elem ...
... and points to a possible source of the lack of clarity in holistic doctrines – namely the refusal of making the degree of dependence explicit. This last feature is especially important if we keep in mind that some holistic theories seem to be trivial in character – if, for example, by “being an elem ...
Propositional/First
... • How can these sentences be represented so that we can infer the third sentence from the first two? ...
... • How can these sentences be represented so that we can infer the third sentence from the first two? ...
In defence of an argument against truthmaker maximalism
... the previous example of ‘consisting of no more than 10 words’ and as in the case of the Liar Sentence, which would mean again its outright inconsistency. But if S ′ is not F , S ′ is again simply true (exactly as in the previous example of ‘consisting of no more than 5 words’) and does not ‘establis ...
... the previous example of ‘consisting of no more than 10 words’ and as in the case of the Liar Sentence, which would mean again its outright inconsistency. But if S ′ is not F , S ′ is again simply true (exactly as in the previous example of ‘consisting of no more than 5 words’) and does not ‘establis ...
Slides
... • In PL we have to create propositional symbols to stand for all or part of each sentence. For example, we might do: P = “person”; Q = “mortal”; R = “Confucius” ...
... • In PL we have to create propositional symbols to stand for all or part of each sentence. For example, we might do: P = “person”; Q = “mortal”; R = “Confucius” ...
Propositional Logic
... • In PL we have to create propositional symbols to stand for all or part of each sentence. For example, we might do: P = “person”; Q = “mortal”; R = “Confucius” ...
... • In PL we have to create propositional symbols to stand for all or part of each sentence. For example, we might do: P = “person”; Q = “mortal”; R = “Confucius” ...
Propositional logic, I
... Inference rules: Typographical rules (they do not use meaning) to construct new sentences from a given group of sentences. Semantics: Interpretation rules that associate sentences in the language with statements in the domain of discourse. Forget meaning. Think of logic as a game. BEWARE: It is easy ...
... Inference rules: Typographical rules (they do not use meaning) to construct new sentences from a given group of sentences. Semantics: Interpretation rules that associate sentences in the language with statements in the domain of discourse. Forget meaning. Think of logic as a game. BEWARE: It is easy ...