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First-Order Theorem Proving and Vampire
First-Order Theorem Proving and Vampire

... http://www.tptp.org contains a large collection of first-order problems. For representing these problems it uses the TPTP syntax, which is understood by all modern theorem provers, including Vampire. In the TPTP syntax this group theory problem can be written down as follows: %---- 1 * x = 1 fof(lef ...
Principia Logico-Metaphysica (Draft/Excerpt)
Principia Logico-Metaphysica (Draft/Excerpt)

Labeled Natural Deduction for Temporal Logics
Labeled Natural Deduction for Temporal Logics

... to ancient Greece, with the works of Aristotle and Diodorus Cronus. However, the birth of modern (symbolic) temporal logic is mainly connected to the name of Prior, who in the late 1950’s developed the so-called tense logics on the model of modal logics, in a work significantly titled “Time and Moda ...
Behavioral Algebraization of Logics
Behavioral Algebraization of Logics

Goal-directed Proof Theory
Goal-directed Proof Theory

Structural Proof Theory
Structural Proof Theory

Predicate Logic
Predicate Logic

1 7.3 calculus with the inverse trigonometric functions
1 7.3 calculus with the inverse trigonometric functions

thèse - IRIT
thèse - IRIT

Everything Else Being Equal: A Modal Logic for Ceteris Paribus
Everything Else Being Equal: A Modal Logic for Ceteris Paribus

... of PL(ϕ Pψ) with respect to the set of all proposition letters. Amplification guarantees that every r in the universe of discourse of a formula that is not directly relevant to the evaluation of a preference subformula is kept constant. This would not be the case, for instance, if given a preference ...
KURT GÖDEL - National Academy of Sciences
KURT GÖDEL - National Academy of Sciences

... (1978) by Quine gives an excellent overview in just under four pages. ...
Sample pages 2 PDF
Sample pages 2 PDF

... a well-formed formula if is syntactically correct. The propositional formulae given in the examples above are all well-formed while, for example, (∧ ‘it is raining’) is not. We will describe well-formed formulae using the following table: ...
proof terms for classical derivations
proof terms for classical derivations

The Premiss-Based Approach to Logical Aggregation Franz Dietrich & Philippe Mongin
The Premiss-Based Approach to Logical Aggregation Franz Dietrich & Philippe Mongin

Logic and Proof
Logic and Proof

... Aristotle observed that the correctness of this inference has nothing to do with the truth or falsity of the individual statements, but, rather, the general pattern: Every A is B. Every B is C. Therefore every A is C. We can substitute various properties for A, B, and C; try substituting the propert ...
SEQUENT SYSTEMS FOR MODAL LOGICS
SEQUENT SYSTEMS FOR MODAL LOGICS

... normal modal logics will not be considered in the present chapter. In relational proof systems the logical object language is associated with a language of relational terms. These terms may contain subterms representing the accessibility relation in possible-worlds models, so that semantic informati ...
x - Homepages | The University of Aberdeen
x - Homepages | The University of Aberdeen

Combinaison des logiques temporelle et déontique pour la
Combinaison des logiques temporelle et déontique pour la

... other hand. Indeed, we have to express for instance the permission to access a resource for a certain period, the obligation to release a resource before a deadline, or the prohibition to execute a task for a too long period. Temporal and deontic logics seem well suited to specify such concepts. In ...
Cut-elimination for provability logics and some results in display logic
Cut-elimination for provability logics and some results in display logic

Notes on the Science of Logic
Notes on the Science of Logic

Harmony, Normality and Stability
Harmony, Normality and Stability

Modal fixpoint logic: some model theoretic questions
Modal fixpoint logic: some model theoretic questions

... of the domain. It is also one of the most expressive logics that is known to be decidable on trees, whether they are binary or unranked (that is, there is no restriction on the number a successors of a node). Hence, it is not surprising that most specification languages are fragments of MSO. This me ...
Functional Dependencies in a Relational Database and
Functional Dependencies in a Relational Database and

Sound and Complete Inference Rules in FOL Example
Sound and Complete Inference Rules in FOL Example

... Let us try resolution to infer Rich(M e)! The standard way of showing that KB ` φ by resolution is to add ¬φ to the KB and show that we can reach the empty clause by repeated application of the resolution rule. In our case, we add ¬Rich(M e). ...
Deductive Databases with Universally Quantified Conditions
Deductive Databases with Universally Quantified Conditions

... a n-ary predicate symbol, t1, ..., tn are terms exactly one of are either constant or variable symbols. a n-ary predicate symbol, t1, ..., tn are terms exactly one of are either constant or variable symbols. ...
1 2 3 4 5 ... 37 >

Propositional formula

In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula.A propositional formula is constructed from simple propositions, such as ""five is greater than three"" or propositional variables such as P and Q, using connectives such as NOT, AND, OR, and IMPLIES; for example:(P AND NOT Q) IMPLIES (P OR Q).In mathematics, a propositional formula is often more briefly referred to as a ""proposition"", but, more precisely, a propositional formula is not a proposition but a formal expression that denotes a proposition, a formal object under discussion, just like an expression such as ""x + y"" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importance.
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