A game semantics for proof search: Preliminary results - LIX
... The proviso † requires that t and s are unifiable and θ is their most general unifier (∆θ is the multiset resulting from applying θ to all formulas in ∆). The proviso ‡ requires that t and s are not unifiable. The free variables of a sequent are also called eigenvariables. Notice that the equality r ...
... The proviso † requires that t and s are unifiable and θ is their most general unifier (∆θ is the multiset resulting from applying θ to all formulas in ∆). The proviso ‡ requires that t and s are not unifiable. The free variables of a sequent are also called eigenvariables. Notice that the equality r ...
A modal perspective on monadic second
... a special class of finite directed graphs we define. Over this class the expressive power of SOPML coincides with that of MSO, whence we easily obtain the desired result that the alternation hierarchy of SOPML is infinite over finite directed graphs. The precise definition of strong first-order redu ...
... a special class of finite directed graphs we define. Over this class the expressive power of SOPML coincides with that of MSO, whence we easily obtain the desired result that the alternation hierarchy of SOPML is infinite over finite directed graphs. The precise definition of strong first-order redu ...
Geometric Modal Logic
... Inference rules: modus ponens, ‘necessitation’ rule (φ/2φ) and rule of uniform substitution (χ(p)/χ[φ/p]). The ensuing system is system T. Further axioms: axiom 4, 2p → 22p, which defines S4 = T + 4, or axiom 5, 3p → 23p, which defines S5. ...
... Inference rules: modus ponens, ‘necessitation’ rule (φ/2φ) and rule of uniform substitution (χ(p)/χ[φ/p]). The ensuing system is system T. Further axioms: axiom 4, 2p → 22p, which defines S4 = T + 4, or axiom 5, 3p → 23p, which defines S5. ...
Substitution and Evaluation
... As expressions become more complicated than the examples above, rules for evaluating these expressions become necessary. When values are used in place of variables, there is a universally agreed upon mathematical sequence, a specific order, in which each operation must be performed to evaluate the r ...
... As expressions become more complicated than the examples above, rules for evaluating these expressions become necessary. When values are used in place of variables, there is a universally agreed upon mathematical sequence, a specific order, in which each operation must be performed to evaluate the r ...
CHAPTER 1. SENTENTIAL LOGIC 1. Introduction In sentential logic
... The truth value of any compound sentence is determined completely by the truth values of its component parts. For example, assuming 2, 7, odd, prime all have their usual meanings then 7 is odd and 2 is odd is false but (7 is odd and 2 is odd) or 2 is prime is true. We will discuss implication later. ...
... The truth value of any compound sentence is determined completely by the truth values of its component parts. For example, assuming 2, 7, odd, prime all have their usual meanings then 7 is odd and 2 is odd is false but (7 is odd and 2 is odd) or 2 is prime is true. We will discuss implication later. ...
The Science of Proof - University of Arizona Math
... The origin of this work was my desire to understand the natural mathematical structure of logical reasoning. When I was a student at the University of Washington I attended lectures of Paul Halmos on algebraic logic, and I found this the beginning of a coherent account [5]. More clarification came f ...
... The origin of this work was my desire to understand the natural mathematical structure of logical reasoning. When I was a student at the University of Washington I attended lectures of Paul Halmos on algebraic logic, and I found this the beginning of a coherent account [5]. More clarification came f ...
Effectively Polynomial Simulations
... boolean formulas, R(f, m) such that when m is at least is said to be weakly automatizable. the size of the shortest B-proof of f , R(f, m) has an A When we say “automatizable” in future, we mean proof of size polynomial in |f | + m. If there also exists a polynomial-time function (again polytime in ...
... boolean formulas, R(f, m) such that when m is at least is said to be weakly automatizable. the size of the shortest B-proof of f , R(f, m) has an A When we say “automatizable” in future, we mean proof of size polynomial in |f | + m. If there also exists a polynomial-time function (again polytime in ...
pdf
... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
Rules of inference
... “It is below freezing now (p). Therefore, it is either below freezing or raining now (q).” “It is below freezing (p). It is raining now (q). Therefore, it is below freezing and it is raining now. “if it rains today (p), then we will not have a barbecue today (q). if we do not have a barbecue t ...
... “It is below freezing now (p). Therefore, it is either below freezing or raining now (q).” “It is below freezing (p). It is raining now (q). Therefore, it is below freezing and it is raining now. “if it rains today (p), then we will not have a barbecue today (q). if we do not have a barbecue t ...
On the Complexity of Resolution-based Proof Systems
... Note that the first set of clauses forces every pigeon to fly to some hole and the second ensures that no hole will be doubly occupied. Therefore, refuting these clauses, that is, proving that they are contradictory, would prove the principle true. Observe that the principle is not expressed by the ...
... Note that the first set of clauses forces every pigeon to fly to some hole and the second ensures that no hole will be doubly occupied. Therefore, refuting these clauses, that is, proving that they are contradictory, would prove the principle true. Observe that the principle is not expressed by the ...
Seventy-five problems for testing automatic
... ATPers in mind that the following list is offered. None of these problems will be the sort whose solution is, of itself, of any mathematical or logical interest. Such ‘open problems’ are regularly published in the Newsletter of the Association for Automated Reasoning. Most (but not all) of my proble ...
... ATPers in mind that the following list is offered. None of these problems will be the sort whose solution is, of itself, of any mathematical or logical interest. Such ‘open problems’ are regularly published in the Newsletter of the Association for Automated Reasoning. Most (but not all) of my proble ...
