Full Text - Institute for Logic, Language and Computation
... viewing syntactical and philosophical considerations. The existence of several kinds of conditional sentences is recognized in the current literature but the consequences are not sufficiently shown. We will investigate here the criteria which allow such a division and illustrate these differences by ...
... viewing syntactical and philosophical considerations. The existence of several kinds of conditional sentences is recognized in the current literature but the consequences are not sufficiently shown. We will investigate here the criteria which allow such a division and illustrate these differences by ...
The Liar Paradox: A Consistent and Semantically Closed Solution
... This thesis develops a new approach to the formal de nition of a truth predicate that allows a consistent, semantically closed de nition within classical logic. The approach is built on an analysis of structural properties of languages that make Liar Sentences and the paradoxical argument possible. ...
... This thesis develops a new approach to the formal de nition of a truth predicate that allows a consistent, semantically closed de nition within classical logic. The approach is built on an analysis of structural properties of languages that make Liar Sentences and the paradoxical argument possible. ...
logic for computer science - Institute for Computing and Information
... ‘advanced’, that are central to modern computer science. In many cases, where proof methods have been specified by non-deterministic sets of rules, we have been more precise than usual by giving algorithms and programs; in other cases we have relied on the background of our students to keep routine ...
... ‘advanced’, that are central to modern computer science. In many cases, where proof methods have been specified by non-deterministic sets of rules, we have been more precise than usual by giving algorithms and programs; in other cases we have relied on the background of our students to keep routine ...
Truth-Functional Logic
... Parentheses and the Method of Induction A statement like A ∧ B ∨ C is ambiguous: is this the conjunction of A and B ∨ C, or is this a disjunction of A ∧ B and C? We will require that our statements are not ambiguous, and we will use parentheses to do so. So, if this statement was meant to be a conj ...
... Parentheses and the Method of Induction A statement like A ∧ B ∨ C is ambiguous: is this the conjunction of A and B ∨ C, or is this a disjunction of A ∧ B and C? We will require that our statements are not ambiguous, and we will use parentheses to do so. So, if this statement was meant to be a conj ...
doc
... (a) Explain what it means to say that a sentence in the predicate calculus is semantically true. Also state what it means for a sequent to be semantically valid in predicate logic. A sentence in the predicate calculus is semantically true iff the sentence is true in very interpretation of the predic ...
... (a) Explain what it means to say that a sentence in the predicate calculus is semantically true. Also state what it means for a sequent to be semantically valid in predicate logic. A sentence in the predicate calculus is semantically true iff the sentence is true in very interpretation of the predic ...
Presuppositions of Compound Sentences
... speaker and the listener. According to the pragmatic conception, the speaker, rather than the sentence he utters, has presuppositions. To presuppose something as a speaker is to take its truth for granted and to assume that the audience does the same. Strictly speaking, it would be meaningless to ta ...
... speaker and the listener. According to the pragmatic conception, the speaker, rather than the sentence he utters, has presuppositions. To presuppose something as a speaker is to take its truth for granted and to assume that the audience does the same. Strictly speaking, it would be meaningless to ta ...
7 LOGICAL AGENTS
... bottomless pits that will trap anyone who wanders into these rooms (except for the wumpus, which is too big to fall in). The only mitigating feature of this bleak environment is the possibility of finding a heap of gold. Although the wumpus world is rather tame by modern computer game standards, it ...
... bottomless pits that will trap anyone who wanders into these rooms (except for the wumpus, which is too big to fall in). The only mitigating feature of this bleak environment is the possibility of finding a heap of gold. Although the wumpus world is rather tame by modern computer game standards, it ...
Predicate logic definitions
... A derivation in PDE is a series of sentences of PLE, each of which is either an assumption or is obtained from previous sentences by one of the rules of PDE. A sentence P of PLE is derivable in PDE from a set Γ of sentences of PLE, written S ` P, iff there exists a derivation in PDE in which all the ...
... A derivation in PDE is a series of sentences of PLE, each of which is either an assumption or is obtained from previous sentences by one of the rules of PDE. A sentence P of PLE is derivable in PDE from a set Γ of sentences of PLE, written S ` P, iff there exists a derivation in PDE in which all the ...
Interplay between Syntax and Semantics during Sentence
... processing (for a more extensive discussion, see Hagoort et al., 1999). Thus, the finding of qualitatively distinct ERP effects for semantic and syntactic processing operations supports the claim that these two levels of language processing are domain specific. However, domain specificity should not ...
... processing (for a more extensive discussion, see Hagoort et al., 1999). Thus, the finding of qualitatively distinct ERP effects for semantic and syntactic processing operations supports the claim that these two levels of language processing are domain specific. However, domain specificity should not ...
sentential logic
... In considering arguments formally, we care about what would be true if the premises were true. Generally, we are not concerned with actual truth values of any particular sentences- whether they are actually true or false. Yet there are some sentences that must be true, just as a matter of logic. Con ...
... In considering arguments formally, we care about what would be true if the premises were true. Generally, we are not concerned with actual truth values of any particular sentences- whether they are actually true or false. Yet there are some sentences that must be true, just as a matter of logic. Con ...
Discrete Mathematics: Chapter 2, Predicate Logic
... the various mathematical entities mentioned in your sentences. For symbols with a known standard meaning, such a lexicon is not important, but if symbols are unfamiliar or are used in unconventional ways, their meaning must be stipulated. Logical symbols such as connectives or quantifiers will alway ...
... the various mathematical entities mentioned in your sentences. For symbols with a known standard meaning, such a lexicon is not important, but if symbols are unfamiliar or are used in unconventional ways, their meaning must be stipulated. Logical symbols such as connectives or quantifiers will alway ...
The Semantic Complexity of some Fragments of English
... This simple observation suggests a programme of work: take a fragment of English delineated in terms which respect the syntax of the language; then determine the computational complexity of deciding satisfiability in that fragment, if, indeed, the fragment is decidable. From this standpoint, the syl ...
... This simple observation suggests a programme of work: take a fragment of English delineated in terms which respect the syntax of the language; then determine the computational complexity of deciding satisfiability in that fragment, if, indeed, the fragment is decidable. From this standpoint, the syl ...
Optimality in Sentence Processing
... theory (Box 12:1) and thus each candidate structure is a fully connected tree with a single root node, like all trees. However, we do not assume that the trees Int produces are all rooted in S (i.e., a sentence node; also labeled as IP or CP in X’ representation). If the initial words of the sentenc ...
... theory (Box 12:1) and thus each candidate structure is a fully connected tree with a single root node, like all trees. However, we do not assume that the trees Int produces are all rooted in S (i.e., a sentence node; also labeled as IP or CP in X’ representation). If the initial words of the sentenc ...
Semantics of PL
... contains. Our book has ‘finite interpretation’ as a distinct category which is just any interpretation in which there are only finitely many things, but in general, there is no real distinction between finite and infinite universes. Informally, we sometimes may say x ranges over people, or numbers, ...
... contains. Our book has ‘finite interpretation’ as a distinct category which is just any interpretation in which there are only finitely many things, but in general, there is no real distinction between finite and infinite universes. Informally, we sometimes may say x ranges over people, or numbers, ...
On Rosser sentences and proof predicates
... acquaintance with Gödels incompleteness results might be useful as well. PA is Peano arithmetic, formulated in your favourite first order logic. Every theory T is assumed to be a sufficiently strong, consistent extension of some fragment of PA. We use ϕ, ψ, χ, . . . for formulas and ϕ for the term ...
... acquaintance with Gödels incompleteness results might be useful as well. PA is Peano arithmetic, formulated in your favourite first order logic. Every theory T is assumed to be a sufficiently strong, consistent extension of some fragment of PA. We use ϕ, ψ, χ, . . . for formulas and ϕ for the term ...
The logic and mathematics of occasion sentences
... specifies the cognitive structures that are taken to contain the primary bearers of TVs. This we call the T HEORY OF C ONTEXTUAL A NCHORING. Secondly, a T HEORY OF R EFERENTIAL K EYING, is needed to specify how the c ...
... specifies the cognitive structures that are taken to contain the primary bearers of TVs. This we call the T HEORY OF C ONTEXTUAL A NCHORING. Secondly, a T HEORY OF R EFERENTIAL K EYING, is needed to specify how the c ...
Automatic Distillation of Musical Structures: Learning the Grammar of Music
... almost identical, can usually be replaced with little change to the music. However, ADIOS also tends to find some disharmonic equivalence classes, which is not common in standard western musical theory. One equivalence class includes chords of C-Major, Bb7-Major and G7-Major, with melody notes from ...
... almost identical, can usually be replaced with little change to the music. However, ADIOS also tends to find some disharmonic equivalence classes, which is not common in standard western musical theory. One equivalence class includes chords of C-Major, Bb7-Major and G7-Major, with melody notes from ...
Logic and the Axiomatic Method
... organize our thoughts in a coherent way. If you gain nothing else from the course than this, you have still gained the greatest gift that mathematics has to offer. I wish to persuade you that a certain statement is true or false by pure reasoning. I could do this by showing you that the ...
... organize our thoughts in a coherent way. If you gain nothing else from the course than this, you have still gained the greatest gift that mathematics has to offer. I wish to persuade you that a certain statement is true or false by pure reasoning. I could do this by showing you that the ...
on partially conservative sentences and interpretability
... every \¡i e F. In §1 this concept for T - 2°+, and Tl°+, is investigated. In §2 results from §1 are applied to interpretability in theories containing arithmetic. ...
... every \¡i e F. In §1 this concept for T - 2°+, and Tl°+, is investigated. In §2 results from §1 are applied to interpretability in theories containing arithmetic. ...
On Perfect Introspection with Quantifying-in
... of an agent can be reduced to the objective ones. In ILL88], it was shown that this result holds even if we weaken the logic in the sense that beliefs are not necessarily closed under (classical) logical consequence. In the first-order case, however, we run into problems because of the phenomenon of ...
... of an agent can be reduced to the objective ones. In ILL88], it was shown that this result holds even if we weaken the logic in the sense that beliefs are not necessarily closed under (classical) logical consequence. In the first-order case, however, we run into problems because of the phenomenon of ...
Soundness and Completeness for Sentence Logic Trees
... negation of the conclusion as its initial sentences. Closed trees are the syntactic objects which need to correspond to the semantic concept of validity. So proving soundness and completeness for the tree method means proving that we have the right sort of correspondence between validity and closed ...
... negation of the conclusion as its initial sentences. Closed trees are the syntactic objects which need to correspond to the semantic concept of validity. So proving soundness and completeness for the tree method means proving that we have the right sort of correspondence between validity and closed ...
Scrambling and Processing: Dependencies
... 1990; Lee, 1993; Tada, 1993; Haider, 1994; Miyagawa, 1997; Bošković and Takahashi, 1998, among others) compete with each other without clear theoretical support for any single theory. This is just the right kind of setting to look for psycholinguistic arguments that may be consistent with one or the ...
... 1990; Lee, 1993; Tada, 1993; Haider, 1994; Miyagawa, 1997; Bošković and Takahashi, 1998, among others) compete with each other without clear theoretical support for any single theory. This is just the right kind of setting to look for psycholinguistic arguments that may be consistent with one or the ...
Notes on `the contemporary conception of logic`
... Any sentence [of logicians’ English] built up using these connectives has a truth-value which depends on the truth values of the constituent sentences. In order to make this dependence apparent, let us apply the name statement form to an expression built up from the sentence letters A, B, C, etc., ...
... Any sentence [of logicians’ English] built up using these connectives has a truth-value which depends on the truth values of the constituent sentences. In order to make this dependence apparent, let us apply the name statement form to an expression built up from the sentence letters A, B, C, etc., ...
1 The Easy Way to Gödel`s Proof and Related Matters Haim Gaifman
... satisfying certain well–defined syntactic conditions. If the language is sufficiently expressive, the syntax, the enumeration of wffs, as well as the notion of provability can be expressed in it. There seems to be no essential obstacle to the construction of a wff ϕk such that, for all n: ...
... satisfying certain well–defined syntactic conditions. If the language is sufficiently expressive, the syntax, the enumeration of wffs, as well as the notion of provability can be expressed in it. There seems to be no essential obstacle to the construction of a wff ϕk such that, for all n: ...
Section
... When evaluating a sentence with multiple quantifiers, don’t fall into the trap of thinking that distinct variables range over distinct objects. In fact, the sentence xyP(x,y) logically implies xP(x,x), and xP(x,x) logically implies xyP(x,y)! ...
... When evaluating a sentence with multiple quantifiers, don’t fall into the trap of thinking that distinct variables range over distinct objects. In fact, the sentence xyP(x,y) logically implies xP(x,x), and xP(x,x) logically implies xyP(x,y)! ...