Basic Concepts of Formal Logic
... apply to the evaluation of reasoning by all persons at all times and places. Two properties of reasoning, in particular, are studied by formal logic: consistency and valid inference. In order to understand what consistency and valid inference are, they must be clearly distinguished from something el ...
... apply to the evaluation of reasoning by all persons at all times and places. Two properties of reasoning, in particular, are studied by formal logic: consistency and valid inference. In order to understand what consistency and valid inference are, they must be clearly distinguished from something el ...
Reading 2 - UConn Logic Group
... since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and !-calculus. ...
... since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and !-calculus. ...
AN EARLY HISTORY OF MATHEMATICAL LOGIC AND
... or Richard Dedekind. I believe this is because Styazhkin believes first, that logic from Leibniz to Peano was largely separate from set theory; and second, he believed that logic after Peano changed radically in its relationship with set theory. This is just the view that I want to combat. The reaso ...
... or Richard Dedekind. I believe this is because Styazhkin believes first, that logic from Leibniz to Peano was largely separate from set theory; and second, he believed that logic after Peano changed radically in its relationship with set theory. This is just the view that I want to combat. The reaso ...
notes
... a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P . That is, P most accurately describes input states for which c either does not terminate or ends up ...
... a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P . That is, P most accurately describes input states for which c either does not terminate or ends up ...
MODAL LANGUAGES AND BOUNDED FRAGMENTS OF
... that is needed in one fell swoop. Thus, our calculus involves no shortening rules, and the proof search space is finite. (In a sense, then, at least as far as quantification is concerned, 'linear logic' is already complete for modal fragments of predicate logic.) This observation suggests yet anoth ...
... that is needed in one fell swoop. Thus, our calculus involves no shortening rules, and the proof search space is finite. (In a sense, then, at least as far as quantification is concerned, 'linear logic' is already complete for modal fragments of predicate logic.) This observation suggests yet anoth ...
page 113 THE AGM THEORY AND INCONSISTENT BELIEF
... logical consequence, any belief is contained in the belief set once a contradictory belief such as A∧¬A is involved. For the logical principle ex contradictione quodlibet (ECQ), that anything follows from inconsistent premises (A, ¬A |= B for any A and B) is valid in classical logic. Consequently, b ...
... logical consequence, any belief is contained in the belief set once a contradictory belief such as A∧¬A is involved. For the logical principle ex contradictione quodlibet (ECQ), that anything follows from inconsistent premises (A, ¬A |= B for any A and B) is valid in classical logic. Consequently, b ...
Dependence Logic
... a certain game 25 times thus producing 25 sequences of moves. A team of 25 agents is created. It may be desirable to know answers to the following kinds of questions: (a) What is the strategy that a player is following, or is he or she following any strategy at all? (b) Is a player using information ...
... a certain game 25 times thus producing 25 sequences of moves. A team of 25 agents is created. It may be desirable to know answers to the following kinds of questions: (a) What is the strategy that a player is following, or is he or she following any strategy at all? (b) Is a player using information ...
Higher Order Logic - Indiana University
... try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foundational aspects of higher order logic, and also to brie y point to some areas of current and potential applications. The chapter falls into two par ...
... try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foundational aspects of higher order logic, and also to brie y point to some areas of current and potential applications. The chapter falls into two par ...
Higher Order Logic - Theory and Logic Group
... try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foundational aspects of higher order logic, and also to brie y point to some areas of current and potential applications. The chapter falls into two par ...
... try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foundational aspects of higher order logic, and also to brie y point to some areas of current and potential applications. The chapter falls into two par ...
ch1_1
... equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
... equal and so are the corresponding angles. Two angles are supplementary if the sum of their measures is 180 degrees. ...
Fichte`s Legacy in Logic
... The proposition, ‘God is omnipotent’ contains two concepts, each of which has its object – God and omnipotence. The small word ‘is’ adds no new predicate, but only serves to posit the predicate in its relation to the subject. If, now, we take the subject (God) with all its predicates (among which is ...
... The proposition, ‘God is omnipotent’ contains two concepts, each of which has its object – God and omnipotence. The small word ‘is’ adds no new predicate, but only serves to posit the predicate in its relation to the subject. If, now, we take the subject (God) with all its predicates (among which is ...
Lecture slides
... Should we worry that p → q is a weak model for: “If p is True then it must be the case that q is True.” We want to use p → q in valid arguments. p → q “if p is True then q is True” p “p is True” q “therefore q is True” Fortunately, we can do this with confidence. Notice the Truth table for “material ...
... Should we worry that p → q is a weak model for: “If p is True then it must be the case that q is True.” We want to use p → q in valid arguments. p → q “if p is True then q is True” p “p is True” q “therefore q is True” Fortunately, we can do this with confidence. Notice the Truth table for “material ...
The Natural Order-Generic Collapse for ω
... order-generic first-order formula ϕ which uses the additional predicates, there is a formula with linear ordering alone which is equivalent to ϕ on all finite databases. Belegradek et al. [1] have extended this result: Instead of o-minimality they consider quasi o-minimality, and instead of finite data ...
... order-generic first-order formula ϕ which uses the additional predicates, there is a formula with linear ordering alone which is equivalent to ϕ on all finite databases. Belegradek et al. [1] have extended this result: Instead of o-minimality they consider quasi o-minimality, and instead of finite data ...
The Herbrand Manifesto
... weaker. In fact, it is stronger. There are more things that are true. We cannot prove them all, but we can prove everything we could prove before. Some may be disturbed by the fact that Herbrand entailment is not semi-decidable. But a similar argument could be leveled against Tarskian semantics. Sem ...
... weaker. In fact, it is stronger. There are more things that are true. We cannot prove them all, but we can prove everything we could prove before. Some may be disturbed by the fact that Herbrand entailment is not semi-decidable. But a similar argument could be leveled against Tarskian semantics. Sem ...
On Dummett`s Pragmatist Justification Procedure
... The logical constants are “→” (implication), “∨” (disjunction), “∧” (conjunction) and “⊥” (absurdity). As usual, “¬” (negation) is defined in terms of the absurdity constant: ¬A ≡ A → ⊥. I use Latin letters (“A”, “B”, “C” etc.) to stand for arbitrary sentences and Greek letters (“Γ” and “∆”) to stan ...
... The logical constants are “→” (implication), “∨” (disjunction), “∧” (conjunction) and “⊥” (absurdity). As usual, “¬” (negation) is defined in terms of the absurdity constant: ¬A ≡ A → ⊥. I use Latin letters (“A”, “B”, “C” etc.) to stand for arbitrary sentences and Greek letters (“Γ” and “∆”) to stan ...
Chapter 3
... Now when we considered 2 as the lattice (2, ∨, ∧) we found that its theory was not that of lattices but rather of distributive lattices. For (2, ∨, ∧, →) we may ask an analogous question: is its theory just that of Heyting algebras, or something larger? Just as with the lattice (2, ∨, ∧), the answer ...
... Now when we considered 2 as the lattice (2, ∨, ∧) we found that its theory was not that of lattices but rather of distributive lattices. For (2, ∨, ∧, →) we may ask an analogous question: is its theory just that of Heyting algebras, or something larger? Just as with the lattice (2, ∨, ∧), the answer ...
Many-Valued Logic
... Suppose we were to retain the obvious classical clauses: v (¬A ) = 1 ⇔ v (A ) = 0 v (¬A ) = 0 ⇔ v (A ) = 1 v (A ∧ B ) = 1 ⇔ v (A ) = v (B ) = 1 v (A ∧ B ) = 0 ⇔ v (A ) = 0 or v (B ) = 0 v (A ∨ B ) = 1 ⇔ v (A ) = 1 or v (B ) = 1 v (A ∨ B ) = 0 ⇔ v (A ) = v (B ) = 0 v (A ⊃ B ) = 1 ⇔ v (A ) = 0 or v (B ...
... Suppose we were to retain the obvious classical clauses: v (¬A ) = 1 ⇔ v (A ) = 0 v (¬A ) = 0 ⇔ v (A ) = 1 v (A ∧ B ) = 1 ⇔ v (A ) = v (B ) = 1 v (A ∧ B ) = 0 ⇔ v (A ) = 0 or v (B ) = 0 v (A ∨ B ) = 1 ⇔ v (A ) = 1 or v (B ) = 1 v (A ∨ B ) = 0 ⇔ v (A ) = v (B ) = 0 v (A ⊃ B ) = 1 ⇔ v (A ) = 0 or v (B ...
x - Homepages | The University of Aberdeen
... Kees van Deemter Slides adapted from Michael P. Frank’s Course Based on the Text Discrete Mathematics & Its Applications ...
... Kees van Deemter Slides adapted from Michael P. Frank’s Course Based on the Text Discrete Mathematics & Its Applications ...
Using linear logic to reason about sequent systems
... relevant here since the scope of ? will always be atomic. Lemma 1. If a sequent has a Forum proof, it has a proof in which there are no occurrences of decide? applied to an atomic formula. Proof Permute all occurrences of decide? involving an atomic formula up in a proof until they reach an instance ...
... relevant here since the scope of ? will always be atomic. Lemma 1. If a sequent has a Forum proof, it has a proof in which there are no occurrences of decide? applied to an atomic formula. Proof Permute all occurrences of decide? involving an atomic formula up in a proof until they reach an instance ...
Using linear logic to reason about sequent systems ?
... possible, and since contexts in Forum are either multisets or sets, we will not be able to represent sequents that make use of lists. It is unlikely, for example, that non-commutative object-logics can be encoded into our linear logic meta theory along the lines we describe below. ...
... possible, and since contexts in Forum are either multisets or sets, we will not be able to represent sequents that make use of lists. It is unlikely, for example, that non-commutative object-logics can be encoded into our linear logic meta theory along the lines we describe below. ...
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 ...
FC §1.1, §1.2 - Mypage at Indiana University
... mulas themselves. But it is the applications that bring the subject to life for most people. We will, of course, cover some applications as we go along. In a sense, though, the real applications of logic include much of computer science and of mathematics itself. Among the fundamental elements of th ...
... mulas themselves. But it is the applications that bring the subject to life for most people. We will, of course, cover some applications as we go along. In a sense, though, the real applications of logic include much of computer science and of mathematics itself. Among the fundamental elements of th ...
Logic for Computer Science. Lecture Notes
... reasoning or, in other words, what are we going to talk about and what language are we going to use. The next step is to associate a precise meaning to basic notions of the language, in order to avoid ambiguities and misunderstandings. Finally we have to state clearly what kind of opinions (sentence ...
... reasoning or, in other words, what are we going to talk about and what language are we going to use. The next step is to associate a precise meaning to basic notions of the language, in order to avoid ambiguities and misunderstandings. Finally we have to state clearly what kind of opinions (sentence ...
Insights into Modal Slash Logic and Modal Decidability
... Suppose the semantics of logics L and L0 are defined relative to pointed models. Logic L is translatable into logic L0 (in symbols L ≤ L0 ) if for every φ ∈ L there is ψφ ∈ L0 such that for all M and w, we have: M, w |= φ iff M, w |= ψφ . And L0 is strictly more expressive than L (in symbols L < L0 ...
... Suppose the semantics of logics L and L0 are defined relative to pointed models. Logic L is translatable into logic L0 (in symbols L ≤ L0 ) if for every φ ∈ L there is ψφ ∈ L0 such that for all M and w, we have: M, w |= φ iff M, w |= ψφ . And L0 is strictly more expressive than L (in symbols L < L0 ...
Decidability for some justification logics with negative introspection
... Artemov et al. [4] introduced the first justification logic with negative introspection. The current formulation, however, of justified negative introspection has been independently developed by Pacuit [21] and Rubtsova [23]. They prove several initial results for justification logics with negative ...
... Artemov et al. [4] introduced the first justification logic with negative introspection. The current formulation, however, of justified negative introspection has been independently developed by Pacuit [21] and Rubtsova [23]. They prove several initial results for justification logics with negative ...