CUED PhD and MPhil Thesis Classes
... connectives ∧, ∨ and optionally constants ⊥, > and classical negation, which yields full nonassociative Lambek calculus (FNL) and its extensions DFNL and BFNL, satisfying the distributive laws for ∧, ∨ or the laws boolean algebras, respectively. Modal nonassociative Lambek calculus (NL♦) is NL enric ...
... connectives ∧, ∨ and optionally constants ⊥, > and classical negation, which yields full nonassociative Lambek calculus (FNL) and its extensions DFNL and BFNL, satisfying the distributive laws for ∧, ∨ or the laws boolean algebras, respectively. Modal nonassociative Lambek calculus (NL♦) is NL enric ...
![overhead 8/singular sentences [ov]](http://s1.studyres.com/store/data/009258618_1-2a98e952bde8fd34c716ae0716ce6df4-300x300.png)
overhead 8/singular sentences [ov]
... - FIRST symbolize the quantifier word: We symbolize UNIVERSAL quantifier words with an individual variable in parentheses: (x) - this is read "for all x" We symbolize EXISTENTIAL quantifier words with a backwards "E" along with an individual variable in parentheses: (x) - this is read "there exists ...
... - FIRST symbolize the quantifier word: We symbolize UNIVERSAL quantifier words with an individual variable in parentheses: (x) - this is read "for all x" We symbolize EXISTENTIAL quantifier words with a backwards "E" along with an individual variable in parentheses: (x) - this is read "there exists ...
PDF
... Now what about the completeness of a tableau? In the propositional case, this meant that the tableau cannot be extended any further, because all formulas have been decomposed. Since the propositional tableau method terminates after finitely many steps, this was an easy thing to define. In the first- ...
... Now what about the completeness of a tableau? In the propositional case, this meant that the tableau cannot be extended any further, because all formulas have been decomposed. Since the propositional tableau method terminates after finitely many steps, this was an easy thing to define. In the first- ...
Propositional Discourse Logic
... not deny its possibility but neither know where to find it nor attempt to do it. Locally meaningful, relative totalities, on the other hand, appear every time we conduct a conversation and our holism relies only on such relative totalities of actual interest. Its essential aspect is possible lack of ...
... not deny its possibility but neither know where to find it nor attempt to do it. Locally meaningful, relative totalities, on the other hand, appear every time we conduct a conversation and our holism relies only on such relative totalities of actual interest. Its essential aspect is possible lack of ...
On the Construction of Analytic Sequent Calculi for Sub
... a) sub-classical logic. Various important and useful non-classical logics can be formalized in this way, with the most prominent example being intuitionistic logic. In general, the resulting logics come at first with no semantics. They might be also unusable for computational purposes, since the new ...
... a) sub-classical logic. Various important and useful non-classical logics can be formalized in this way, with the most prominent example being intuitionistic logic. In general, the resulting logics come at first with no semantics. They might be also unusable for computational purposes, since the new ...
Maximal Introspection of Agents
... our choice of epistemic principles should not depend on our choice of base theory. For one thing, the epistemic principles only give general properties of belief (or knowledge), and our choice of these should only depend on what kind of “modality” (or propositional attitude) Bi is supposed to captur ...
... our choice of epistemic principles should not depend on our choice of base theory. For one thing, the epistemic principles only give general properties of belief (or knowledge), and our choice of these should only depend on what kind of “modality” (or propositional attitude) Bi is supposed to captur ...
PS12
... 1. Query goals appear in the root node of the proof tree. 2. Choose a current goal (Prolog's policy the leftmost goal). 3. Choose a rule to the current goal. (Prolog's policy by top to bottom program order). 4. Variables in rules are (consecutively) renamed before applying the unification algorithm. ...
... 1. Query goals appear in the root node of the proof tree. 2. Choose a current goal (Prolog's policy the leftmost goal). 3. Choose a rule to the current goal. (Prolog's policy by top to bottom program order). 4. Variables in rules are (consecutively) renamed before applying the unification algorithm. ...
Ascribing beliefs to resource bounded agents
... and is usually defined as the agent knowing all logical tautologies and all the consequences of its knowledge. Logical omniscience is problematic when attempting to build realistic models of agent behaviour, as closure under logical consequence implies that deliberation takes no time. Most logical ...
... and is usually defined as the agent knowing all logical tautologies and all the consequences of its knowledge. Logical omniscience is problematic when attempting to build realistic models of agent behaviour, as closure under logical consequence implies that deliberation takes no time. Most logical ...
Ways Things Can`t Be
... only if there is some world w where w A. It is impossible otherwise. Clearly, contradictions of the form A ∧ ∼ A are impossible. Other propositions might be impossible too. It might be that in the model, there is no possible world w such that w p, for some atomic proposition p. This is allowed b ...
... only if there is some world w where w A. It is impossible otherwise. Clearly, contradictions of the form A ∧ ∼ A are impossible. Other propositions might be impossible too. It might be that in the model, there is no possible world w such that w p, for some atomic proposition p. This is allowed b ...
Using Modal Logics to Express and Check Global Graph Properties
... known. There are a series of standard results that state that frames that are “similar” in a number of ways must agree on the validity of formulas. We can then use these results to prove that a certain property cannot be expressed by any formula in the basic graph logic. To do this, we take two fram ...
... known. There are a series of standard results that state that frames that are “similar” in a number of ways must agree on the validity of formulas. We can then use these results to prove that a certain property cannot be expressed by any formula in the basic graph logic. To do this, we take two fram ...
Formal Theories of Truth INTRODUCTION
... of contradiction. From the intuitive standpoint the truth of all those theorems is itself already a proof of the general principle; this principle represents, so to speak, an ‘infinite logical product’ of those special theorems. But this does not at all mean that we can actually derive the principle ...
... of contradiction. From the intuitive standpoint the truth of all those theorems is itself already a proof of the general principle; this principle represents, so to speak, an ‘infinite logical product’ of those special theorems. But this does not at all mean that we can actually derive the principle ...
Soundness and completeness
... Theorem.[Completeness] If Γ |= A, then Γ ⊢ A is provable in ND. As with most logics, the completeness of propositional logic is harder (and more interesting) to show than the soundness. We shall spend the next few slides with the completeness proof. ...
... Theorem.[Completeness] If Γ |= A, then Γ ⊢ A is provable in ND. As with most logics, the completeness of propositional logic is harder (and more interesting) to show than the soundness. We shall spend the next few slides with the completeness proof. ...
Gödel on Conceptual Realism and Mathematical Intuition
... find a specific proposition G that is true but unprovable in that system. The basic elementary part of logic known as ordinary first-order logic is complete. Gödel’s actual completeness result had the effect of minimizing the distinction between model-theoretical and proof-theoretical concepts (the ...
... find a specific proposition G that is true but unprovable in that system. The basic elementary part of logic known as ordinary first-order logic is complete. Gödel’s actual completeness result had the effect of minimizing the distinction between model-theoretical and proof-theoretical concepts (the ...
How to Prove Properties by Induction on Formulas
... properties about all formulas using structural induction. “Structural induction” refers to induction principles that work directly on the structure of recursively generated objects, rather than using natural numbers to measure properties like the height or length of an object. In this note, we will: ...
... properties about all formulas using structural induction. “Structural induction” refers to induction principles that work directly on the structure of recursively generated objects, rather than using natural numbers to measure properties like the height or length of an object. In this note, we will: ...
Conditional Statements
... emphasize which part is the hypothesis and which is the conclusion. Hint: Turn the subject into the hypothesis. Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. ...
... emphasize which part is the hypothesis and which is the conclusion. Hint: Turn the subject into the hypothesis. Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. ...
Factoring Out the Impossibility of Logical Aggregation
... any kind. Literals pe are those formulas which are either p.v. (e p = p) or negations of p.v. (e p = :p): The notation :e p means :p in the former case and p in the latter; it accords with the general convention adopted here that double negations cancel. When we wish to emphasize that the literal va ...
... any kind. Literals pe are those formulas which are either p.v. (e p = p) or negations of p.v. (e p = :p): The notation :e p means :p in the former case and p in the latter; it accords with the general convention adopted here that double negations cancel. When we wish to emphasize that the literal va ...
vmcai - of Philipp Ruemmer
... Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based on a sequent calculus, the proof rules are extended by labelled formulae and annotations that reduce, at the root of a closed proof, to interpolants. In earlier w ...
... Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based on a sequent calculus, the proof rules are extended by labelled formulae and annotations that reduce, at the root of a closed proof, to interpolants. In earlier w ...
Week 3: Logical Language
... Mathematical English It is vitally important at this stage to understand the exact meaning of the logical symbols that have been introduced, and how they are connected to the English language, which is usually less precise than it should be. In most settings, mathematical statements – including most ...
... Mathematical English It is vitally important at this stage to understand the exact meaning of the logical symbols that have been introduced, and how they are connected to the English language, which is usually less precise than it should be. In most settings, mathematical statements – including most ...
3.3 Inference
... Proof by contrapositive inference is an example of what we call indirect inference. We have actually seen another example indirect inference, the method of proof by contradiction. Recall that in our proof of Euclid’s Division Theorem we began by assuming that the theorem was false. We then chose amo ...
... Proof by contrapositive inference is an example of what we call indirect inference. We have actually seen another example indirect inference, the method of proof by contradiction. Recall that in our proof of Euclid’s Division Theorem we began by assuming that the theorem was false. We then chose amo ...