• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Lecture Notes on the Lambda Calculus
Lecture Notes on the Lambda Calculus

... information than classical ones, and in particular, they allow one to compute solutions to problems (as opposed to merely knowing the existence of a solution). The resulting algorithms can be useful in computational mathematics, for instance in ...
On the meanings of the logical constants and the justifications of the
On the meanings of the logical constants and the justifications of the

On the Meaning of the Logical Constants and the
On the Meaning of the Logical Constants and the

PDF
PDF

... You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
The Logic of Compound Statements
The Logic of Compound Statements

... called proposition forms or formulas built from propositional variables (atoms), which represent simple propositions and symbols representing logical connectives  Proposition or propositional variables: p, q,… each can be true or false Examples: p=“Socrates is mortal” q=“Plato is mortal” ...
Algebraizing Hybrid Logic - Institute for Logic, Language and
Algebraizing Hybrid Logic - Institute for Logic, Language and

Handling Exceptions in nonmonotonic reasoning
Handling Exceptions in nonmonotonic reasoning

LPF and MPLω — A Logical Comparison of VDM SL and COLD-K
LPF and MPLω — A Logical Comparison of VDM SL and COLD-K

... to be expressed as formulae of MPLω . This was first sketched in [KR89, Section 4] and later worked out in detail by Renardel de Lavalette in [Ren89]. If A is a formula, then the term ιx : S (A) can be formed which is called a description. Its intended meaning is the unique value x of sort S that sa ...
Introduction to mathematical arguments
Introduction to mathematical arguments

Rich Chapter 5 Predicate Logic - Computer Science
Rich Chapter 5 Predicate Logic - Computer Science

... But a major motivation for choosing to use logic at all is that if we use logical statements as a way of representing knowledge, then we have available a good way of reasoning with that knowledge. Determining the validity of a proposition in propositional logic is straightforward, although it may be ...
Problems on Discrete Mathematics1
Problems on Discrete Mathematics1

... We use Dx , Dy to denote the domains of x and y, respectively. Note that Dx and Dy do not have to be the same. In the above example, P (3, 2) is the proposition 3 ≥ 22 with truth value F . Similarly, Q(Boo, dog) is a proposition with truth value T if there is a dog named Boo. Note: Any proposition i ...
First-Order Intuitionistic Logic with Decidable Propositional
First-Order Intuitionistic Logic with Decidable Propositional

Fine`s Theorem on First-Order Complete Modal Logics
Fine`s Theorem on First-Order Complete Modal Logics

Essentials Of Symbolic Logic
Essentials Of Symbolic Logic

... discoveries was not realized at the time they were made. The general belief that all the important logical discoveries have been made by Aristotle naturally tended to prevent philosophers from assessing any new discovery at it’s true value. The undeveloped state of the mathematical sciences prior to ...
Notes on Modal Logic - Stanford University
Notes on Modal Logic - Stanford University

... • Alethic Reading: 2ϕ means ‘ϕ is necessary’ and 3ϕ means ‘ϕ is possible’. • Deontic Reading: 2ϕ means ‘ϕ is obligatory’ and 3ϕ means ‘ϕ is permitted’. In this literature, typically ‘O’ is used instead of ‘2’ and ‘P ’ instead of ‘3’. • Epistemic Reading: 2ϕ means ‘ϕ is known’ and 3ϕ means ‘ϕ is cons ...
Formal Foundations of Computer Security
Formal Foundations of Computer Security

... P1 , P2 , P3 , and the events - all the actions taken, say e1 , e2 , e3 , ... Each action has a location apparent from its definition, say loc(e). Some of the events are comparable ei < ej and others aren’t, e.g. imagine two processes that never communicate e1 , e2 , ... at i and e0i , e02 , ... at ...
notes
notes

... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given 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 ...
article - British Academy
article - British Academy

... prove that I cannot prove that 0 = 1. Then the F can prove that I cannot prove that 0 = 1. It doesn’t follow that the F can prove that the F cannot prove that 0 = 1. There are two separable issues here. First, the existence of deviant provability operators, with which the theorem does not go through ...
Knowledge of Logical Truth Knowledge of Logical Truth
Knowledge of Logical Truth Knowledge of Logical Truth

... The question is then whether those truths are derivable from any set of premises. All other possible premises imagined will be additions to E, so the question is whether adding any set of those could ruin the implication. That is, we need: For all S and p, if E├ p then E,S ├ p. So, it looks like the ...
Default Logic (Reiter) - Department of Computing
Default Logic (Reiter) - Department of Computing

... • α follows from (D, S W ) by ‘brave’/‘credulous’ reasoning when α in any extension of (D, W ): α ∈ ext(D, W ); • α follows from (D, T W ) by ‘cautious’/‘sceptical’ reasoning when α in all extensions of (D, W ): α ∈ ext(D, W ). ...
Introduction to Modal and Temporal Logic
Introduction to Modal and Temporal Logic

... Lemma 1 For any Kripke model hW, R, ϑi, any w ∈ W and any formula ϕ, either ϑ(w, ϕ) = t or else ϑ(w, ϕ) = f . Proof: Pick any Kripke model hW, R, ϑi, any w ∈ W , and any formula ϕ. Proceed by induction on the length l of ϕ. Base Case l = 1: If ϕ is an atomic formula p, either ϑ(w, p) = t or ϑ(w, p) ...
Views: Compositional Reasoning for Concurrent Programs
Views: Compositional Reasoning for Concurrent Programs

P,Q
P,Q

full text (.pdf)
full text (.pdf)

... In all these examples, the proofs we give are quite short and involve establishing a coinductive step analogous to the inductive step in proofs by induction. What is missing is the final argument that the proof is a valid application of the coinduction principle; but it is not necessary to include th ...
On the Notion of Coherence in Fuzzy Answer Set Semantics
On the Notion of Coherence in Fuzzy Answer Set Semantics

... as least fixpoint of a logic program, it has been due to an excess of information in the program (possibly erroneous information). As a result, rejecting noncoherent interpretations seems convenient as well. An important remark is that coherence can be interpreted with an empirical sense and that th ...
< 1 ... 7 8 9 10 11 12 13 14 15 ... 57 >

Natural deduction

In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the ""natural"" way of reasoning. This contrasts with the axiomatic systems which instead use axioms as much as possible to express the logical laws of deductive reasoning.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report