Section 1.1: The Language of Sentential Logic

• The role of logical symbols in translation from/into English does not change.
• The meaning of non-logical symbols (parameters) is not fixed.
• It is assumed that no symbol is a finite sequence of other symbols.
• English sentences are different from their translations into the formal language, for two reasons, first same sentence symbols can be used for different English sentences in different contexts, and, second, English sentences are usually presumed to be either true or false, while sentence symbols may have different true/false values depending on their interpretations in different contexts.

1. A sentence symbol is a wff.
2. If $\alpha$ and $\beta$ are wffs, then so are $\neg\alpha$ , $\alpha\wedge\beta$ , $\alpha\vee\beta$ , $\alpha\rightarrow\beta$ , $\alpha\leftrightarrow\beta$ .

1. A wff $\alpha$ is the expression obtained at the last step of a finite sequence of expressions $<\epsilon_{1},\ldots,\epsilon_{n}>$ ,
2. where $\epsilon_{i}$ is either a sentence symbol, or an expression obtained by a formula-building operation, i.e. $\mathcal{E}_{\neg}(\epsilon_{j})$ or $\mathcal{E}_{\square}(\epsilon_{j},\epsilon_{k})$ , where $j,k<i$ and $\square\in\{\wedge,\vee,\rightarrow,\leftrightarrow\}$ .