The Semantic Complexity of some Fragments of English
... A BSTRACT. By a fragment of a natural language we mean a subset of that language equipped with a semantics which translates its sentences into some formal system such as first-order logic. The familiar concepts of satisfiability and entailment can be defined for any such fragment in a natural way. T ...
... A BSTRACT. By a fragment of a natural language we mean a subset of that language equipped with a semantics which translates its sentences into some formal system such as first-order logic. The familiar concepts of satisfiability and entailment can be defined for any such fragment in a natural way. T ...
On Decidability of Intuitionistic Modal Logics
... the intuitionistic and modal accessibility relations can be expressed using mso definable closure operators. We illustrate this method by showing that it works for various truth definitions for modalities and various conditions on the intuitionistic and modal accessibility occurring in the literatur ...
... the intuitionistic and modal accessibility relations can be expressed using mso definable closure operators. We illustrate this method by showing that it works for various truth definitions for modalities and various conditions on the intuitionistic and modal accessibility occurring in the literatur ...
Ways Things Can`t Be
... which includes all three beliefs? We have already seen the Lewis/Stalnaker account, which is to “chunk” the belief set into consistent compartments. There are no worlds at which the three-way conjunction is true, but there are worlds at which any pair is true. Our belief set is quarantined into cons ...
... which includes all three beliefs? We have already seen the Lewis/Stalnaker account, which is to “chunk” the belief set into consistent compartments. There are no worlds at which the three-way conjunction is true, but there are worlds at which any pair is true. Our belief set is quarantined into cons ...
A Concise Introduction to Mathematical Logic
... The way of arguing about formal languages and theories is traditionally called the metatheory. An important task of a metatheoretic analysis is to specify procedures of logical inference by so-called logical calculi, which operate purely syntactically. There are many different logical calculi. The c ...
... The way of arguing about formal languages and theories is traditionally called the metatheory. An important task of a metatheoretic analysis is to specify procedures of logical inference by so-called logical calculi, which operate purely syntactically. There are many different logical calculi. The c ...
Modal Logic - Web Services Overview
... 2. The starting point, once again, is Aristotle, who was the first to study the relationship between modal statements and their validity. 3. However, the great discussion it enjoyed in the Middle Ages. 4. The official birth date of modal logic is 1921, when Clarence Irving Lewis wrote a famous essay ...
... 2. The starting point, once again, is Aristotle, who was the first to study the relationship between modal statements and their validity. 3. However, the great discussion it enjoyed in the Middle Ages. 4. The official birth date of modal logic is 1921, when Clarence Irving Lewis wrote a famous essay ...
From Syllogism to Common Sense Normal Modal Logic
... significantly shorten proofs, which is our main concern here. ‣ Example: Congruence rules. ‣ The general form of a rule is the following: ...
... significantly shorten proofs, which is our main concern here. ‣ Example: Congruence rules. ‣ The general form of a rule is the following: ...
![overhead 12/proofs in predicate logic [ov]](http://s1.studyres.com/store/data/011612593_1-f0437b45ca3df4f633ddcc6197d427a6-300x300.png)
overhead 12/proofs in predicate logic [ov]
... NOW the two remaining rules: - the rule for getting rid of the existential quantifier: Existential Instantiation (EI) (preliminary version) (x)x a - the rule for introducing the universal quantifier: Universal Generalization (UG) (preliminary version) a (x)x - these rules should seem much less ...
... NOW the two remaining rules: - the rule for getting rid of the existential quantifier: Existential Instantiation (EI) (preliminary version) (x)x a - the rule for introducing the universal quantifier: Universal Generalization (UG) (preliminary version) a (x)x - these rules should seem much less ...
Infinity 1. Introduction
... actually count up to, such as 200, rather than practically inaccessible numbers such as 100100 . You resolve to found mathematics entirely on what is feasible. Again, the question recurs: how many feasible numbers are there? The answer, surely, is ‘infeasibly many’. All three of these positions (fin ...
... actually count up to, such as 200, rather than practically inaccessible numbers such as 100100 . You resolve to found mathematics entirely on what is feasible. Again, the question recurs: how many feasible numbers are there? The answer, surely, is ‘infeasibly many’. All three of these positions (fin ...
Formal Foundations of Computer Security
... order. This is a very spare and abstract account of some of the expressible relationships in an execution of a distributed system. Given an execution (or computation) comp, we can pick out the locations say P1 , P2 , P3 , and the events - all the actions taken, say e1 , e2 , e3 , ... Each action has ...
... order. This is a very spare and abstract account of some of the expressible relationships in an execution of a distributed system. Given an execution (or computation) comp, we can pick out the locations say P1 , P2 , P3 , and the events - all the actions taken, say e1 , e2 , e3 , ... Each action has ...
Factoring Out the Impossibility of Logical Aggregation
... formalized as sets of formulas in some logical language, and then investigate the e¤ect of imposing axiomatic conditions on this mapping. Among the results obtained is a striking impossibility theorem that abstractly generalizes the doctrinal paradox (Pauly and van Hees, 2006; see also Dietrich, 200 ...
... formalized as sets of formulas in some logical language, and then investigate the e¤ect of imposing axiomatic conditions on this mapping. Among the results obtained is a striking impossibility theorem that abstractly generalizes the doctrinal paradox (Pauly and van Hees, 2006; see also Dietrich, 200 ...
Diagrammatic Reasoning in Separation Logic
... Separation logic is used for reasoning about low-level imperative programs that manipulate pointer data structures. It enables the writing of concise proofs of correctness of the specifications of simple programs, and such proofs have been successfully automated. When reasoning informally about sepa ...
... Separation logic is used for reasoning about low-level imperative programs that manipulate pointer data structures. It enables the writing of concise proofs of correctness of the specifications of simple programs, and such proofs have been successfully automated. When reasoning informally about sepa ...
Fine`s Theorem on First-Order Complete Modal Logics
... discreteness property that between any two points there are only finitely many other points. Earlier, Kripke [42] had observed that Dummet’s formula is not preserved by the Jónsson–Tarski representation of modal algebras. This is an algebraic formulation of the non-canonicity of this formula. The a ...
... discreteness property that between any two points there are only finitely many other points. Earlier, Kripke [42] had observed that Dummet’s formula is not preserved by the Jónsson–Tarski representation of modal algebras. This is an algebraic formulation of the non-canonicity of this formula. The a ...
Argument construction and reinstatement in logics for
... In recent years, researchers in nonmonotonic logic have turned increasing attention to formal systems in which nonmonotonic reasoning is analyzed through the study of interactions among competing defeasible arguments; a survey appears in Prakken and Vreewsijk (forthcoming). These argument systems ar ...
... In recent years, researchers in nonmonotonic logic have turned increasing attention to formal systems in which nonmonotonic reasoning is analyzed through the study of interactions among competing defeasible arguments; a survey appears in Prakken and Vreewsijk (forthcoming). These argument systems ar ...
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 ...
Properties of Independently Axiomatizable Bimodal Logics
... − ⊗ − : (EK)2 → EK2 . ⊗ is a -homomorphism in both arguments. There are certain easy properties of this map which are noteworthy. Fixing the second argument we can study the map − ⊗ M : EK → EK2 . This is a -homomorphism. The map −2 : EK2 → EK : L 7→ L2 will be shown to almost the inverse of − ...
... − ⊗ − : (EK)2 → EK2 . ⊗ is a -homomorphism in both arguments. There are certain easy properties of this map which are noteworthy. Fixing the second argument we can study the map − ⊗ M : EK → EK2 . This is a -homomorphism. The map −2 : EK2 → EK : L 7→ L2 will be shown to almost the inverse of − ...
On The Expressive Power of Three-Valued and Four
... Bilattices were further investigated by Fitting, who used them for extending some well known logics (like Kleene 3-valued logics) and for logic programming (see, e.g., [Fi90, Fi91, Fi94]). In [AA96] the set D is also generalized to what is called there a bi lter, and bilattices-based logics are intr ...
... Bilattices were further investigated by Fitting, who used them for extending some well known logics (like Kleene 3-valued logics) and for logic programming (see, e.g., [Fi90, Fi91, Fi94]). In [AA96] the set D is also generalized to what is called there a bi lter, and bilattices-based logics are intr ...
Logic and the Axiomatic Method
... There should be no problem in reaching mutual understanding so long as we use terms familiar to both and use them consistently. If I use an unfamiliar term, you have the right to demand a definition of this term. Definitions cannot be given arbitrarily; they are s ...
... There should be no problem in reaching mutual understanding so long as we use terms familiar to both and use them consistently. If I use an unfamiliar term, you have the right to demand a definition of this term. Definitions cannot be given arbitrarily; they are s ...
07.1-Reasoning
... that a wumpus is in 1,1 1,3 or 2,2. We use the resolution with the sentence telling us that 2,2 does not contain a wumpus and we get 1,1 or 1,3 contain a wumpus • We repeat the unit resolution rule with the new sentence 1,1 or 1,3 contain a wumpus and the sentence telling us that 1,1 does not contai ...
... that a wumpus is in 1,1 1,3 or 2,2. We use the resolution with the sentence telling us that 2,2 does not contain a wumpus and we get 1,1 or 1,3 contain a wumpus • We repeat the unit resolution rule with the new sentence 1,1 or 1,3 contain a wumpus and the sentence telling us that 1,1 does not contai ...
connections to higher type Recursion Theory, Proof-Theory
... has to be viewed as the formalization of the abstract notion of function, including higher type and higher order functions; thus, the results of the formal theory often turn out to be relevant in applications or in the general understanding of functional behaviour. By this and by the connections dis ...
... has to be viewed as the formalization of the abstract notion of function, including higher type and higher order functions; thus, the results of the formal theory often turn out to be relevant in applications or in the general understanding of functional behaviour. By this and by the connections dis ...
Document
... Arguments in Proposi:onal Logic • A argument in proposi:onal logic is a sequence of proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is ...
... Arguments in Proposi:onal Logic • A argument in proposi:onal logic is a sequence of proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is ...
On the Notion of Coherence in Fuzzy Answer Set Semantics
... When I is a non-coherent L-interpretation, then there exists a propositional symbol p such that either I(∼ p) > ∼ I(p) or I(∼ p) and ∼ I(p) are incomparable elements in L. In both cases a non-coherent interpretation implies a contradiction with the negation meta-rule. Is this contradiction given by ...
... When I is a non-coherent L-interpretation, then there exists a propositional symbol p such that either I(∼ p) > ∼ I(p) or I(∼ p) and ∼ I(p) are incomparable elements in L. In both cases a non-coherent interpretation implies a contradiction with the negation meta-rule. Is this contradiction given by ...
Document
... - Informally, the purpose of unification is to find what the common objects are. Such goal may be acomplished by purely syntactic means, through processing of the terms appearing in the common predicates. - A term is composed of one or more symbols from • Variable symbols (convention: starting with ...
... - Informally, the purpose of unification is to find what the common objects are. Such goal may be acomplished by purely syntactic means, through processing of the terms appearing in the common predicates. - A term is composed of one or more symbols from • Variable symbols (convention: starting with ...
A Proof Theory for Generic Judgments
... These two approaches are, however, at odds with each other. Consider, for example, the problem of representing restriction of names or nonces using ∀ quantification. (The following example can be dualized in the event that a logical specification uses ∃ quantification instead of ∀, as in, for exampl ...
... These two approaches are, however, at odds with each other. Consider, for example, the problem of representing restriction of names or nonces using ∀ quantification. (The following example can be dualized in the event that a logical specification uses ∃ quantification instead of ∀, as in, for exampl ...
A Proof Theory for Generic Judgments: An extended abstract
... local signatures of a sequent) cannot be seen if one is simply attempting to “evaluate” hc∀ logical programs by determining the goals that they can prove. A difference between these two quantifiers only starts to appear (for hc∀ definitions) if more interesting goals are considered: for example, in ...
... local signatures of a sequent) cannot be seen if one is simply attempting to “evaluate” hc∀ logical programs by determining the goals that they can prove. A difference between these two quantifiers only starts to appear (for hc∀ definitions) if more interesting goals are considered: for example, in ...
Digital Logic and the Control Unit
... Chapter 4 – Digital Logic and the Control Unit This chapter will cover digital logic and its use to build a control unit for a computer. The function of the control unit is to interpret the binary machine language and cause the computer to do what each instruction directs, even if it is not what the ...
... Chapter 4 – Digital Logic and the Control Unit This chapter will cover digital logic and its use to build a control unit for a computer. The function of the control unit is to interpret the binary machine language and cause the computer to do what each instruction directs, even if it is not what the ...
Jesús Mosterín
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Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.