Divide and congruence applied to eta-bisimulation
... versions of execution sequences. Van Glabbeek [8] classified equivalences for processes that take into account the internal action τ . Here we focus on one such equivalence, called η-bisimulation [1]. In general a semantic equivalence induced by a transition system specification is not a congruence, ...
... versions of execution sequences. Van Glabbeek [8] classified equivalences for processes that take into account the internal action τ . Here we focus on one such equivalence, called η-bisimulation [1]. In general a semantic equivalence induced by a transition system specification is not a congruence, ...
Logical Inference and Mathematical Proof
... Lemma: less important theorem used to prove other theorems. Corollary: theorem that trivially follows another theorem. ...
... Lemma: less important theorem used to prove other theorems. Corollary: theorem that trivially follows another theorem. ...
FC §1.1, §1.2 - Mypage at Indiana University
... takes propositions as basic and considers how they can be combined and manipulated. This branch of logic has surprising application to the design of the electronic circuits that make up computers. Logic gets more interesting when we consider the internal structure of propositions. In English, a prop ...
... takes propositions as basic and considers how they can be combined and manipulated. This branch of logic has surprising application to the design of the electronic circuits that make up computers. Logic gets more interesting when we consider the internal structure of propositions. In English, a prop ...
Lectures on Proof Theory - Create and Use Your home.uchicago
... of the principles of logic to be used in deriving theorems from the axioms, so that logic itself could be axiomatized. In this case, too, the timing was just right: the analysis of logic in Frege’s Begriffsschrift was just what was required. (There was a remarkable meeting here of supply and demand. ...
... of the principles of logic to be used in deriving theorems from the axioms, so that logic itself could be axiomatized. In this case, too, the timing was just right: the analysis of logic in Frege’s Begriffsschrift was just what was required. (There was a remarkable meeting here of supply and demand. ...
Many-Valued Models
... logic L defined by a set of axioms and rules, Γ `L α means, in general, that there is proof in L of α from the premises in Γ. The subscript may be omitted when obvious from the context. If Γ is empty we say that α is a theorem. The propositional three-valued logic known as L3 was first proposed by J ...
... logic L defined by a set of axioms and rules, Γ `L α means, in general, that there is proof in L of α from the premises in Γ. The subscript may be omitted when obvious from the context. If Γ is empty we say that α is a theorem. The propositional three-valued logic known as L3 was first proposed by J ...
Basic Metatheory for Propositional, Predicate, and Modal Logic
... A formal system S consists of a formal language, a formal semantics, or model theory, that defines a notion of meaning for the language, and a proof theory, i.e., a set of syntactic rules for constructing arguments — sequences of formulas — deemed valid by the semantics.1 In this section, we define ...
... A formal system S consists of a formal language, a formal semantics, or model theory, that defines a notion of meaning for the language, and a proof theory, i.e., a set of syntactic rules for constructing arguments — sequences of formulas — deemed valid by the semantics.1 In this section, we define ...
term rewriting.
... to show that some statements (often called a conjecture, goal, conclusion) is a logical consequence of a set of statements (often called hypothesis, assumptions or axioms). The ATP in CafeOBJ is based on (Prover9). Most of the logic problems on this course use the ATP. We set up problems such as Por ...
... to show that some statements (often called a conjecture, goal, conclusion) is a logical consequence of a set of statements (often called hypothesis, assumptions or axioms). The ATP in CafeOBJ is based on (Prover9). Most of the logic problems on this course use the ATP. We set up problems such as Por ...
PROVING THE CORRECTNESS OF REGULA DETERMINISTIC
... Considering the diversity in language, notation and rigor which one finds in the relevant literature we are forced into adlpting, besides a simple programming language, an equally simple language for describing the types of correctness considered anl-,$the proof methods themselves. We have chosen to ...
... Considering the diversity in language, notation and rigor which one finds in the relevant literature we are forced into adlpting, besides a simple programming language, an equally simple language for describing the types of correctness considered anl-,$the proof methods themselves. We have chosen to ...
INTERMEDIATE LOGIC – Glossary of key terms
... A set of logical operators is truth-functionally complete if and only if all possible combinations of true and false are derivable using only those logical operators, i.e. any truth-functional proposition can be written using only those logical operators. In digital logic, a truth-functionally compl ...
... A set of logical operators is truth-functionally complete if and only if all possible combinations of true and false are derivable using only those logical operators, i.e. any truth-functional proposition can be written using only those logical operators. In digital logic, a truth-functionally compl ...
A Revised Concept of Safety for General Answer Set Programs
... by saying that a rule is safe if any variable in the rule also appears in its positive body – this condition will be referred here as DLP safety. Programs are safe if all their rules are safe. The safety of a program ensures that its answer sets coincide with the answer sets of its ground version a ...
... by saying that a rule is safe if any variable in the rule also appears in its positive body – this condition will be referred here as DLP safety. Programs are safe if all their rules are safe. The safety of a program ensures that its answer sets coincide with the answer sets of its ground version a ...
22c:145 Artificial Intelligence
... formal grammar. S , the logic’s semantics is a formal specification of how to assign meaning in the “real world” to the elements of L. R, the logic’s inference system, is a set of formal derivation rules over L. ...
... formal grammar. S , the logic’s semantics is a formal specification of how to assign meaning in the “real world” to the elements of L. R, the logic’s inference system, is a set of formal derivation rules over L. ...
Quantified Equilibrium Logic and the First Order Logic of Here
... answer set semantics, the underlying logic is the least strong negation extension of HT, denoted by N5 . As equilibrium logic is defined for arbitrary propositional formulas it yields an extension of the usual syntax of (ground) answer set programs. It also provides a useful logical foundation for an ...
... answer set semantics, the underlying logic is the least strong negation extension of HT, denoted by N5 . As equilibrium logic is defined for arbitrary propositional formulas it yields an extension of the usual syntax of (ground) answer set programs. It also provides a useful logical foundation for an ...
Recall... Venn Diagrams Disjunctive normal form Disjunctive normal
... For each row (i.e., assignment) with output (i.e., interpretation) of T, write down the formula that uses only AND and NOT and has interpretation T only for that assignment. Write down the disjunction of these formulae (i.e., using “OR”). ...
... For each row (i.e., assignment) with output (i.e., interpretation) of T, write down the formula that uses only AND and NOT and has interpretation T only for that assignment. Write down the disjunction of these formulae (i.e., using “OR”). ...
Second-Order Logic of Paradox
... in going along the number series from 0 to the n for which Xn takes the value False, we must at some step go from a number in the extension to one not in the extension. But this is enough to give the second conjunct of the antecedent one of the values False or Both, and again this will give the whol ...
... in going along the number series from 0 to the n for which Xn takes the value False, we must at some step go from a number in the extension to one not in the extension. But this is enough to give the second conjunct of the antecedent one of the values False or Both, and again this will give the whol ...
WRITING PROOFS Christopher Heil Georgia Institute of Technology
... There are several ways to write a proof of the theorem “If statement A is true then statement B is true.” We’ll discuss several of them in these pages. It may not be obvious at first which variety of proof to use, but a good rule of thumb is to try a direct proof first. A direct proof. Start by assu ...
... There are several ways to write a proof of the theorem “If statement A is true then statement B is true.” We’ll discuss several of them in these pages. It may not be obvious at first which variety of proof to use, but a good rule of thumb is to try a direct proof first. A direct proof. Start by assu ...
